Question

Solve the problem.

Answer 1

Answer:

560

Step-by-step explanation:

You must use a combination:

$_nC_k=\dfrac{n!}{k!(n-k)!}$

We have n = 16, k = 3.

Substitute:

$_{16}C_3=\dfrac{16!}{3!(16-3)!}=\dfrac{13!\cdot14\cdot15\cdot16}{2\cdot3\cdot13!}\qquad\text{cancel}\ 13!\\\\=\dfrac{14\cdot15\cdot16}{2\cdot3}=\dfrac{7\cdot5\cdot16}{1}=560$