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mathmath333
 one year ago
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mathmath333
 one year ago
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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} & \normalsize \text{A squad consists of 16 cricketers including Sachin and Rahul. }\hspace{.33em}\\~\\ & \normalsize \text{ In how many ways can the team of 11 cricketers be selected such that,}\hspace{.33em}\\~\\ & \normalsize \text{If Sachin is selected then Rahul is dropped and }\hspace{.33em}\\~\\ & \normalsize \text{if Rahul is selected then Sachin is dropped .}\hspace{.33em}\\~\\ \end{align}}\)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2There are three possible kinds of situations can you guess them:

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1there are 2 possiblities

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Question can be interpreted in many ways... ok.. tell me what your two possibilities are...

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1Is S is there R is not vice versa

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Since you can only make a team without one or without the other or without both, think of making a team of 11 out of 15 (no Sachin) and a team of 11 out of 15 (no Rahul).

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2then what about both of them are not in the team?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2isn't the answer simply \[\binom{16}{11}  \binom{14}{11}\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(2(_{15}C_{11})\)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 yes indeed that's another way of doing it...

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2It's much simpler than my method...:)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2@mathmath333 did you get ganeshie's one?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1u mean this one \(\Large \dbinom{16}{11}  \dbinom{14}{9}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it is 14 choose 11 not 14 choose 9

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1but in book it is given this \(\Large \dbinom{16}{11}  \dbinom{14}{9}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1any way i didn't get how that comes

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2it is \(\color{red}{16}\) choose 11 not 14 choose 9

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ok but how did u get this answer \(\dbinom{16}{11}  \dbinom{14}{11}\)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2\( \dbinom{16}{11}\) means number of all teams that can be made without considering the condition.. ok?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Then we just have to remove the number of teams where there are S and R both , right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Ahh right, @amilapsn thanks for catching :)

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Then we are left with: 1.teams where there is not S or R 2.teams with only S 3 teams with only R Condition fulfilled...

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1Then we just have to remove the number of teams where there are S and R both this will be done by \(\dbinom{14}{11}\) ?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Yes. Because We've already chosen dravid and thendulkar so we only have to choose anothe nine players out of the rest(14).. Got that?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1and by other method can u tell me 1.teams where there is not S or R 2.teams with only S 3 teams with only R

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.21we've choose 11 out of 14 2we've already chosen S so we have to make sure that R is no there so now we have to choose 10 out of 12 3the same as 2 we've to choose 10 out of 12

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.12we've already chosen S so we have to make sure that R is no there so now we have to choose 10 out of \(\color{red}{12}\) 3the same as 2 we've to choose 10 out of \(\color{red}{12}\) how does \(\color{red}{12}\) comes

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Let's consider the second situation... After choosing S how much players we are left with?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2then can we get R to the team?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Then how much we've to consider?

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2So we've to choose 10 out of 14... (omg my bad that 12 should be 14... sorry for that mistake)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1then by the same logic wolfram gives this false http://www.wolframalpha.com/input/?i=is+%5Cbinom%7B16%7D%7B11%7D%5Cbinom%7B14%7D%7B11%7D%3D%5Cbinom%7B14%7D%7B10%7D%2B%5Cbinom%7B14%7D%7B10%7D%2B%5Cbinom%7B14%7D%7B11%7D+%3F

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1while this is given true http://www.wolframalpha.com/input/?i=is+%5Cbinom%7B16%7D%7B11%7D%5Cbinom%7B14%7D%7B9%7D%3D%5Cbinom%7B14%7D%7B10%7D%2B%5Cbinom%7B14%7D%7B10%7D%2B%5Cbinom%7B14%7D%7B11%7D+%3F

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2wait a sec... Let me see...

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Ok so what's the problem? We are alright, know?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\dbinom{16}{11}\dbinom{14}{11}\) u said earlier that this is correct but wolfram isn't matching it with the other way

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2that second 11 should be nine: I've said that:\[\text{Yes. Because We've already chosen dravid and thendulkar so we only have to choose}\] \[\text{anothe nine players out of the rest(14).. Got that?}\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ok lol i missed that comment earlier completely thanks

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2hows the test between india and lanka going

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2We won the 1st one you know... It was a legendary match due to Chandimal's playing.. Today match is also a very important for all Sri Lankans because it is the final match of Sanga. We'll miss him so much...

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1In the question why we didn't include the case both sachin and rahul are selected.

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2Because the it's said in the question:\[\large \color{black}{\begin{align} & \normalsize \text{A squad consists of 16 cricketers including Sachin and Rahul. }\hspace{.33em}\\~\\ & \normalsize \text{ In how many ways can the team of 11 cricketers be selected such that,}\hspace{.33em}\\~\\ & \normalsize \text{If Sachin is selected then Rahul is dropped and }\hspace{.33em}\\~\\ & \normalsize \text{if Rahul is selected then Sachin is dropped .}\hspace{.33em}\\~\\ \end{align}}\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1by the way india lost 1st test against lanka

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1but it was also not stated that both sachin and rahul won't be selected, then also we add it

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2But it doesn't break the condition right? We have to account for all situations without breaking the condition..

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1but y it dont break the condition

dan815
 one year ago
Best ResponseYou've already chosen the best response.3TotalWays  Ways of sachin and Rahul

dan815
 one year ago
Best ResponseYou've already chosen the best response.3when you to 16 Choose 11 right now in all those combinations it includes the one where both of them are selected that is the only part we have to subtract

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2That's the nature of "if". Have you done logic @mathmath333 ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.3so 16 Choose 11  14 Choose 9

dan815
 one year ago
Best ResponseYou've already chosen the best response.3there are a couple other ways of adding the different cases, this is one way

dan815
 one year ago
Best ResponseYou've already chosen the best response.3another way is to add the cases of no sachin and rahul then only sachin then only rahul

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2\[\href{ https://en.wikipedia.org/wiki/Material_conditional {\huge p\Rightarrow q}\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ok thanks i will look at this logic thing and interpretation of "if"

amilapsn
 one year ago
Best ResponseYou've already chosen the best response.2It's pretty simple you'll get it easily.

dan815
 one year ago
Best ResponseYou've already chosen the best response.32*(14 Choose10) + 14 choose 11 ^ ^________no rahul and sachil ' only rahul + only sachin also should work

dan815
 one year ago
Best ResponseYou've already chosen the best response.3you can actually go on to show this actually always true 2*(14 Choose10) + 14 choose 11 = 16 choose 11  14 choose 9 2*(n choose k) + n choose (k+1) = (n+2) choose (k+1)  n choose(k1)

dan815
 one year ago
Best ResponseYou've already chosen the best response.3if u like that sorta thing lol.. try proving that
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