A group of eight grade 11 and five grade 13 students wish to be on the senior prom committee. The committee will consist of three students. What is the probability that only grade 12 students will be elected, assuming that all students have an equal chance of being elected?
1 answer
There are a total of $8 + 5 = 13$ students from which to choose the committee members. Since only grade 12 students can be elected, there are 5 grade 12 students from which to choose the committee members. The probability that only grade 12 students will be elected is $\dfrac{\binom{5}{3}}{\binom{13}{3}} = \boxed{\dfrac{10}{143}}$.