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Levart [38]
3 years ago
14

A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they ch

oose the 15 questions?
a. 15,504

b. 20,145

c. 23,670

d. 25,890
Mathematics
1 answer:
sveticcg [70]3 years ago
7 0
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
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