The total number of ways of picking r objects out of n, is given by the formula:
[tex]C(n, r)= \frac{n!}{(n-r)!r!} [/tex]
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:
[tex]C(20, 15)= \frac{20!}{(20-15)!15!}= \frac{20!}{15!*5!}= \frac{20*19*18*17*16*15!}{15!*5!}= [/tex]
[tex]\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[/tex]
Answer: A
