Statistics probability problem: From a class of 15 students, find the following:

Question

a) The number of combinations, if a team of five (5) students is chosen.

b) Find the probability that a particular combination of a five-student team will be selected.

c) In how many unique ways can the 15 students be arranged?

Answer 1

Hello Jack,

a) For the first student out of 15 chosen for the team there are 15 possibilities. For the next chosen, there will be 14 possibilities. For the third, there will be 13 possibilities, and so on, until you have the 5 students chosen. To solve this you take:

15 x 14 x 13 x 12 x 11 = 32,760 possible combinations

b) For this, they are looking for only one combination out of the entire number of combinations possible, so the answer would be 1/32,760.

c) For this, they are not choosing only a 5-student team. They want to know how they can arrange the total 15 students. You think of this the same way as part "a", only now, you use all 15 students. This is a called a factorial:

15 x 14 x 13 x 12...all the way down. Another way to write this is "15!" and there should be a "!" button on your calculator. Type it in and you get:

1,307,674,368,000 total combinations