Question

A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?
a. 15,504

b. 20,145

c. 23,670

d. 25,890

Answer 1

The total number of ways of picking r objects out of n, is given by the formula:

$C(n, r)= \frac{n!}{(n-r)!r!}$

where a! is "a factorial", defined as a!=1*2*3*...*(a-1)*a

We are picking 15 objects (questions) out of 20, so substitute r=15 and n=20 in the formula:

$C(20, 15)= \frac{20!}{(20-15)!15!}= \frac{20!}{15!*5!}= \frac{20*19*18*17*16*15!}{15!*5!}=$



$\frac{20*19*18*17*16}{5!}= \frac{20*19*18*17*16}{5*4*3*2}= \frac{19*18*17*16}{3*2}=19*3*17*16=15,504$


Answer: A