In the same order as the given statements:
false
false
true
false
By definition of the binomial coefficient,
[tex]{}_nC_0 = \dfrac{n!}{0!(n-0)!} = \dfrac{n!}{n!} = 1[/tex]
[tex]{}_nC_1 = \dfrac{n!}{1!(n-1)!} = \dfrac{n(n-1)!}{(n-1)!} = n[/tex]
[tex]{}_nC_{n-1} = \dfrac{n!}{(n-1)!(n-(n-1))!} = \dfrac{n!}{(n-1)!1!} = \dfrac{n(n-1)!}{(n-1)!}=n[/tex]
[tex]{}_nC_n = \dfrac{n!}{n!(n-n)!} = \dfrac{n!}{n!0!} = 1[/tex]
