The choir club at a local school is running a field to a waterpark. There are 6 parks the club is considering. The director has asked the members to each pick three to narrow down the list of possibilities before making a final decision. How many different possibilities are there for the list of three? A. 20 B. 150 C. 30 D. 120

Accepted Solution

The formula [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex], where r! is 1*2*3*...r
is the formula which gives us the total number of ways of forming groups of r objects out of n objects.
for example, given 10 objects, there are C(10,6) ways of forming groups of 6, out of the 10 objects.
Thus, there are C(6, 3) many ways of forming different triples out of 6.
[tex]C(6, 3)= \frac{6!}{3!(6-3)!}=\frac{6!}{3!3!}=\frac{6\cdot5\cdot4\cdot3!}{3!3!}=\frac{6\cdot5\cdot4}{3!}=\frac{6\cdot5\cdot4}{3\cdot2\cdot1}=5\cdot4=20[/tex]
Answer: A.20