Question

Evaluate C(6, 6).

answer choices:

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0
1

Answer 1

`C(6,6)=\dbinom66=(6!)/(6!(6-6)!)=\frac1{0!}=\frac11=1`

Answer 2

Option (c) is correct.

C(6, 6) = 1

Explanation:

Given : C(6, 6)

We have to evaluate the value of C(6, 6) and choose the correct from the given options.

Consider the given C(6, 6)

Since,
`^nC_r` gives the number of subsets of r elements out of n elements. and is given by

`nCr=(n!)/(r!\left(n-r\right)!)`

Here, n = r = 6

`=(6!)/(6!\left(6-6\right)!)`

Simplify, we have,

`=(6!)/(6!\left(0\right)!)=1`

Thus, C(6, 6) = 1