Question

There are 15 qualified applicants for 3 trainee positions in a fast-food management program. How many different groups of trainees can be selected?

During the Computer Daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. There are 8 different software packages from which to select. How many different groups of software packages can be selected?

Answer 1

(1) g​​​​​​​​​​iven that

Total positions of trainee = 3

Total qualified applicants = 15

We have to find the number of different groups (or combinations) of 3 applicants out of 15

Now, 3 persons out of 15 may be selected in

15C3 ways.

So, the total number of different groups of trainees

= 15C3

= 15!/3!×12!

=(15×14×13)/(3×2×1)

=5×7×13

=455

(2) given that

   Total number of available packages = 8

  total number of packages customer can choose = 3

therefore, total number of different group of 3 packages may be chosen in 8C3  ways.

I.e

8C3

= 8!/3!×5!

=(8×7×6)/(3×2×1)

=56

Therefore, 56 different group of packages may be selected.