Question

Which statement about the simplified binomial expansion of (a b)n, where n is a positive integer, is true? The value of the binomial coefficient nC0 is n – 1 for all values of n. The values of nC1 and nCn–1 are equal to 1. The values of nC0 and nCn are equal to 1. The value of the binomial coefficient nC1 is n – 1 for all values of n.

Answer 1

In the same order as the given statements:

false

false

true

false

By definition of the binomial coefficient,

`{}_nC_0 = (n!)/(0!(n-0)!) = (n!)/(n!) = 1`

`{}_nC_1 = (n!)/(1!(n-1)!) = (n(n-1)!)/((n-1)!) = n`

`{}_nC_(n-1) = (n!)/((n-1)!(n-(n-1))!) = (n!)/((n-1)!1!) = (n(n-1)!)/((n-1)!)=n`

`{}_nC_n = (n!)/(n!(n-n)!) = (n!)/(n!0!) = 1`

Answer 2

C.

Step-by-step explanation: