Question

Evaluate C(5, 0)
A.0
B.1
C.5

Answer 1

C(5, 0) = 1

B is the correct option.

Explanation:

We have to find the value of C(5, 0).

The formula for combination is given by

`C(n,r)=(n!)/(r!(n-r))!`

Here, we have

n = 5

r = 0

Thus, we have

`C(5,0)=(5!)/(0!(5-0)!)`

We know that 0! = 1. Thus, we have

`C(5,0)=(5!)/(1\cdot5!)\\\\C(5,0)=1`

Therefore, we have C(5, 0) = 1

B is the correct option.

Answer 2

There is 1 way to choose none of 5. The appropriate choice is
B. 1


_____
C(n, k) = n!/(k!(n-k)!)
C(5,0) = 5!/(0!(5-0)!) = 1/0! = 1/1 = 1 . . . . . 0! ≡ 1.