arindameducationusc
  • arindameducationusc
Challenge and also a help..... Check image for question
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
arindameducationusc
  • arindameducationusc
arindameducationusc
  • arindameducationusc
1 Attachment
arindameducationusc
  • arindameducationusc
@ganeshie8 uploaded

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

ganeshie8
  • ganeshie8
look at the 10th row in pascal's triangle : |dw:1438086192297:dw|
ganeshie8
  • ganeshie8
We want to find \(x\) such that \[\large ^{10}C_{x-1} - 3 *^{10}C_{x}~\gt~ 0\]
arindameducationusc
  • arindameducationusc
yes i m looking
ganeshie8
  • ganeshie8
|dw:1438086392992:dw|
arindameducationusc
  • arindameducationusc
yes >0 , understood that because sqare root function and denominator
ganeshie8
  • ganeshie8
notice that 45-3*10 > 0 10-3*1 > 0 1 - 3*0 > 0 so, x = 9, 10, 11 are fine
arindameducationusc
  • arindameducationusc
The answer is none of these... so I am confused
ganeshie8
  • ganeshie8
x = 8 doesn't work because 120 - 3*45 < 0 similarly x>11 doesn't work because 0 - 3*0 = 0
ganeshie8
  • ganeshie8
answer is \(a\) to my knowledge
arindameducationusc
  • arindameducationusc
let me analyse once, give me some time then I may ask you if you have no problem @ganeshie8
ganeshie8
  • ganeshie8
sure
ganeshie8
  • ganeshie8
http://www.wolframalpha.com/input/?i=solve+%2810+choose+%28x-1%29%29+-+3*%2810+choose+x%29+%3E+0+over+integers
arindameducationusc
  • arindameducationusc
Is this the language for combinations? Thats interesting.... hmmm...
arindameducationusc
  • arindameducationusc
solve (10 choose (x-1)) - 3*(10 choose x) > 0 over integers Can you explain this sentence with respect ot combination?
arindameducationusc
  • arindameducationusc
#to#
ganeshie8
  • ganeshie8
\(\large ^nC_r\) is read as \(\large n~~\text{choose}~~r\)
ganeshie8
  • ganeshie8
it is called binomial coefficient and represented by symbol : \[\large \binom{n}{r}\]
arindameducationusc
  • arindameducationusc
Each of the different groups or selections which can be made by taking some or all of a number of things(irrespective of order) //Can you please elaborate this sentence
arindameducationusc
  • arindameducationusc
// Its for Combination
arindameducationusc
  • arindameducationusc
45-3*10 > 0 You checked this for 9?
ganeshie8
  • ganeshie8
yes that is for x = 9
ganeshie8
  • ganeshie8
suppose you went for shopping and liked 5 shirts
arindameducationusc
  • arindameducationusc
ok
ganeshie8
  • ganeshie8
but you can only buy 3 of them
arindameducationusc
  • arindameducationusc
ok
ganeshie8
  • ganeshie8
how many ways are there to choose 3 shirts from the 5 shirts ?
ganeshie8
  • ganeshie8
for definiteness, lets call the shirts : \(a,~b,~c,~d,~e\)
arindameducationusc
  • arindameducationusc
calculations say 10
ganeshie8
  • ganeshie8
can you list them all ?
arindameducationusc
  • arindameducationusc
ok go on... nice
arindameducationusc
  • arindameducationusc
no, I don't have that strong concept.... I would definitely understand from you.... nice....
ganeshie8
  • ganeshie8
no, just list them all, its a simple counting problem
ganeshie8
  • ganeshie8
you can buy the shirts \(a,b,c\) or \(b,c,d\) or \(c,d,e\) or ... try listing them all
arindameducationusc
  • arindameducationusc
okay ... abc acd bed bcd ade bec cde aeb
arindameducationusc
  • arindameducationusc
more two
ganeshie8
  • ganeshie8
looks two are missing yeah
arindameducationusc
  • arindameducationusc
I am trying :P
arindameducationusc
  • arindameducationusc
bae
arindameducationusc
  • arindameducationusc
no no not bae
ganeshie8
  • ganeshie8
``` {a,b,c} {a,b,d} {a,c,d} {b,c,d} {a,b,e} {a,c,e} {b,c,e} {a,d,e} {b,d,e} {c,d,e} ```
ganeshie8
  • ganeshie8
\(\large ^{5}C_3\) gives the number of ways you can choose 3 shirts from 5
arindameducationusc
  • arindameducationusc
Thank you.... any method to find the terms in order... like you easily sound out the 10. suppose 16 or 24... any trick is there?
arindameducationusc
  • arindameducationusc
##found##
ganeshie8
  • ganeshie8
i hope you're familiar with the formula for computing \(^5C_3\) : \[^5C_3 = \dfrac{5!}{3!(5-3)!} =\dfrac{5!}{3!*2!}= \dfrac{5\times 4\times 3\times 2\times 1}{3\times 2\times 1*2\times 1} = 10\]
arindameducationusc
  • arindameducationusc
yes yes.... ofcourse
arindameducationusc
  • arindameducationusc
I am talking about counting.. thats hard! :P
ganeshie8
  • ganeshie8
`Thank you.... any method to find the terms in order... like you easily sound out the 10. suppose 16 or 24... any trick is there?` hey i didnt get what you're asking..
arindameducationusc
  • arindameducationusc
suppose abcdefgh and we have to choose 3 pairs then is there any way by counting? Like suppose I want to view all possibilities
ganeshie8
  • ganeshie8
you want see the entire list of 56 choices ? ``` {a,b,c} {a,b,d} {a,c,d} {b,c,d} {a,b,e} {a,c,e} {b,c,e} {a,d,e} {b,d,e} {c,d,e} {a,b,f} {a,c,f} {b,c,f} {a,d,f} {b,d,f} {c,d,f} {a,e,f} {b,e,f} {c,e,f} {d,e,f} {a,b,g} {a,c,g} {b,c,g} {a,d,g} {b,d,g} {c,d,g} {a,e,g} {b,e,g} {c,e,g} {d,e,g} {a,f,g} {b,f,g} {c,f,g} {d,f,g} {e,f,g} {a,b,h} {a,c,h} {b,c,h} {a,d,h} {b,d,h} {c,d,h} {a,e,h} {b,e,h} {c,e,h} {d,e,h} {a,f,h} {b,f,h} {c,f,h} {d,f,h} {e,f,h} {a,g,h} {b,g,h} {c,g,h} {d,g,h} {e,g,h} {f,g,h} ```
ganeshie8
  • ganeshie8
as you can see its not so pleasant to list them all... why would you want to do that lol
arindameducationusc
  • arindameducationusc
ofcourse it is unpleasant! but Maths is Maths.... but can you tell me how did you do it?
arindameducationusc
  • arindameducationusc
Can Wolfram do this?
ganeshie8
  • ganeshie8
https://jsfiddle.net/ganeshie8/r2hjr3js/1/
arindameducationusc
  • arindameducationusc
Thank you so much for giving your precious time.... :)
ganeshie8
  • ganeshie8
comb(n, set) lists all the combinations of size "n" from the set "set"
ganeshie8
  • ganeshie8
but trust me, you almost never want to list all the possibilities in math most of the time you only want the total number of choices, not the list.
arindameducationusc
  • arindameducationusc
ya its working.... thank you....
arindameducationusc
  • arindameducationusc
Ok got it! :P

Looking for something else?

Not the answer you are looking for? Search for more explanations.