Question

In how many ways can a committee of 4 be chosen from a group of 9 people?

Answer 1

do you know about combinations... are are you just seeking answers so you can pass a test

Answer 2

i dont know combinations

Answer 3

chose 4 out of 9

Answer 4

ok... then it makes it hard to answer this question...as that's what is needed

Answer 5

9C4=ans

Answer 6

@Megan30400

Answer 7

so you are wanting help to understand them... or you just want answers..?

Answer 8

yes i need help

Answer 9

ok... a combination is a counting technique that finds how many ways r items can be selected from a group on n items...

there is a formula that uses factorial notation.

the factorial notation is simply a way of writing mutiplications...

and its written

n! = n x (n -1) x (n -2) x .... 3 x 2 x 1

so

4! = 4 x 3 x 2 x 1 = 24

5! = 5 x 4 x 3 x 2 x 1 = 120

the formula for selecting r objects from a group of n is

\[^nC_{r} = \frac{n!}{r!(n - r)!}\]

so in your question n = 9 and r = 4

so you have

\[^9C_{4} = \frac{9!}{4!(9 - 4)!} = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(4 \times 3 \times 2 \times 1)\times(5 \times 4 \times 3\times 2\times 1)}\]

which can be simplified to

\[^9C_{4} = \frac{9 \times8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}\]

which gives the answer of 126

the nice thing about recognising a combination is that you calculator has an inbuilt function that does the calculation for you.