A project manager oversees 12 employees. How many ways can the employees be divided into four groups of three?

Step-by-step explanation:

To choose for the first group

1st grouping

the number to select from is 12

and we want to group into 4

12C4= C(12,4)= 12!/4!(12-4)!

= 12!/4!8!

=12*11*10*9*8!/4!8!

=12*11*10*9/4*3*2*1

=11880/24

=495

2nd grouping

the number to select from is 8

and we want to group into 4

8C4= C(8,4)= 8!/4!(8-4)!

= 8!/4!4!

=8*7*6*5*4!/4!4!

=8*7*6*5*/4*3*2*1

= 1680/24

=70

3rd grouping

the number to select from is 4

and we want to group into 4

4C4= C(4,4)= 4!/4!(4-4)!

= 4!/4!

=1

495∗70∗1=34650 ways

the total number of ways to choose three groups, when group order matters is 34650 ways

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