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

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)