mathmath333
  • mathmath333
Counting question
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{There are 7 people and 4 chairs. }\hspace{.33em}\\~\\ & \normalsize \text{In how many ways can the chairs be occupied.}\hspace{.33em}\\~\\ \end{align}}\)
amilapsn
  • amilapsn
We can do that in two steps. 1st step: Choosing 4 people out of 7(Combination ) 2nd step: Seating them.(Permutation)
mathmath333
  • mathmath333
is it 4!

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More answers

amilapsn
  • amilapsn
In my method the answer will be this.(Giving the same as nnesha's result): \(\huge ^7C_4\times 4!\)
mathmath333
  • mathmath333
1st step: Choosing 4 people out of 7(Combination ) 2nd step: Seating them.(Permutation) How to implement this
amilapsn
  • amilapsn
\[\huge \ldots=P_{(7,4)} \]
ganeshie8
  • ganeshie8
i like amilapsn's method, but here is an alternative that Nnesha is talking about : you look at 4 chairs, the first chair can have any one of the 7 persons : 7 ways after that, the second chair can have any one of the remaining 6 persons : 6 ways after that, the third chair can have any one of the remaining 5 persons : 5 ways after that, the fourth chair can have any one of the remaining 4 persons : 4 ways so total seating arrangements = 7*6*5*4
ganeshie8
  • ganeshie8
the problem is equivalent to that of finding number of 4 letters words using 7 different letters
mathmath333
  • mathmath333
i think it as only 4 persons can be seated and the 4 persons can be arranged in 4! ways
amilapsn
  • amilapsn
Simplicity @ganeshie8 :D lol
ganeshie8
  • ganeshie8
4! is true if you just have 4 chairs
amilapsn
  • amilapsn
....and only 4 people..
mathmath333
  • mathmath333
yes i just have 4 chairs
ganeshie8
  • ganeshie8
** 4! is true if you just have 4 chairs and 4 people
amilapsn
  • amilapsn
You can take a simple example like 4 people and 3chairs and get the feeling @mathmath333
amilapsn
  • amilapsn
people ABCD ok? All possible ways: ABC ACB ABD ADB ACD ADC .... ... Fill in the blanks and you've get the feeling....
mathmath333
  • mathmath333
is there any website that shows permutations and combinations list
amilapsn
  • amilapsn
python has got the function permutations in itertools module.
mathmath333
  • mathmath333
ABC ACB ABD ADB ACD ADC BCD BDC
ganeshie8
  • ganeshie8
you may use this for combinations https://jsfiddle.net/ganeshie8/r2hjr3js/4/
mathmath333
  • mathmath333
nice
mathmath333
  • mathmath333
it gave this for abcdefg and 4 comb {a,b,c,d} {a,b,c,e} {a,b,d,e} {a,c,d,e} {b,c,d,e} {a,b,c,f} {a,b,d,f} {a,c,d,f} {b,c,d,f} {a,b,e,f} {a,c,e,f} {b,c,e,f} {a,d,e,f} {b,d,e,f} {c,d,e,f} {a,b,c,g} {a,b,d,g} {a,c,d,g} {b,c,d,g} {a,b,e,g} {a,c,e,g} {b,c,e,g} {a,d,e,g} {b,d,e,g} {c,d,e,g} {a,b,f,g} {a,c,f,g} {b,c,f,g} {a,d,f,g} {b,d,f,g} {c,d,f,g} {a,e,f,g} {b,e,f,g} {c,e,f,g} {d,e,f,g}
ganeshie8
  • ganeshie8
right you should get 7C4 = 35 combinations
ganeshie8
  • ganeshie8
for permutations, notice that each of that combination above can be permuted in 4! ways so number of permutations = 35*4!
mathmath333
  • mathmath333
is this question same as "In how many ways can a 4 digit number be formed using digits "1,2,3,4,5,6,7"
amilapsn
  • amilapsn
yep... If you aren't allowed to use the same number twice.
mathmath333
  • mathmath333
ok thnx
mathmath333
  • mathmath333
from the past 2 weeks i m getting this very annoying bug I have to reload the page every time to type and my question gets changed to this page
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ganeshie8
  • ganeshie8
you're not alone, everybody is facing that issue @Astrophysics is there any fix yet ?
amilapsn
  • amilapsn
me too...
mathmath333
  • mathmath333
lol how can so many people tolerate this
mathmath333
  • mathmath333
previuosly it happened only once in an hour but recently it get to on every long text i type

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