Question

15, Evaluate 6 choose 4.

Answer 1

Answer:  The required result is 15.

Step-by-step explanation:  We are given to evaluate the following :

"6 choose 4".

Since we are to choose 4 from 6, so we have to use the combination of 6 different things chosen 4 at a time.

We know that

the formula for the combination of n different things chosen r at a time is given by

$^nC_r=\dfrac{n!}{r!(n-r)!}.$

For the given situation, n = 6  and  r = 4.

Therefore, we get

$^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6!}{4!2!}=\dfrac{6\times5\times4!}{4!\times2\times1}=15.$

Thus, the required result is 15.