There are 15 qualified applicants for 5 trainee positions in a fast-food program. How many groups of trainees can be selected?

I have a feeling that the answer is 75 but I'm not too sure. Any help is appreciated. Thank you!

The first trainee can be any one of 15 people, the second 14, and so on.

Assembling one group of five from 15 folks can be done 15!/10! ways.

Now if you are looking for how many groups can be formed from 15, then the answer is three groups, of five each.

The solution that Bob has given you is correct on the assumption that there are definite positions in the group of 5 people that are selected.

If there is no order in the group and we simply want to have groups of 5 trainees, then the solution would be 15(Choose)5 or
15!/(10!5!) = 3003

15/5=3 . 3 groups of 5

Well, since it's a fast-food program, you could say that they're looking for a "fry-endly" group of trainees. But let's get serious for a moment.

If there are 15 qualified applicants for 5 trainee positions, you want to find out how many groups of trainees can be selected, assuming no order matters.

To do this, we can use a combination formula. The number of combinations of selecting r objects from a set of n objects is given by n C r, which is calculated as n! / (r! * (n-r)!).

In this case, we want to select groups of 5 trainees from a total of 15 qualified applicants. So the formula becomes 15 C 5, which is equal to 15! / (5! * (15-5)!) = 3003.

So there are "3003 reasons" to be excited about the number of possible groups of trainees that can be selected.

To calculate the number of groups of trainees that can be selected, you can use the combination formula.

The formula for calculating combinations is nCr, where n represents the total number of people and r represents the number of people in each group.

In this case, there are 15 qualified applicants and you want to select 5 trainees per group.

You can calculate the number of groups of trainees using the combination formula as follows:

C(15, 5) = 15! / (5! * (15-5)!)

C(15, 5) = 15! / (5! * 10!)

C(15, 5) = (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)

C(15, 5) = 3003

Therefore, there are 3003 groups of trainees that can be selected from the 15 qualified applicants for the 5 trainee positions.

To calculate the number of groups that can be selected, you can use the combination formula known as "n choose k," which is the same as the binomial coefficient. In this case, you have 15 applicants and need to choose 5 for each group.

The formula for combination is n! / (k! * (n - k)!), where n is the total number of items and k is the number of items being chosen.

In your case, you have 15 applicants and need to choose 5 for each group.

The formula becomes:
15! / (5! * (15 - 5)!)

Simplifying this expression:
15! / (5! * 10!)

! denotes the factorial function, which means multiplying a number by all the positive whole numbers less than it. For example, 5! is equal to 5 * 4 * 3 * 2 * 1.

So, for the numerator:
15! = 15 * 14 * 13 * 12 * 11 * 10!
And for the denominator:
5! = 5 * 4 * 3 * 2 * 1

Canceling out the common terms in the numerator and denominator:
15 * 14 * 13 * 12 * 11 * 10! / (5 * 4 * 3 * 2 * 1 * 10!)

10! can be canceled out from both numerator and denominator:
15 * 14 * 13 * 12 * 11 / (5 * 4 * 3 * 2 * 1)

Performing the calculations:
15 * 14 * 13 * 12 * 11 = 360,360
5 * 4 * 3 * 2 * 1 = 120

So, the number of groups that can be selected is:
360,360 / 120 = 3,003

Therefore, you can select 3,003 groups of trainees from the 15 qualified applicants.