Question

Suppose we want to divide the 10 dogs into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. how many ways can we form the groups such that fluffy is in the 3-dog group and nipper is in the 5-dog group?

Answer 1

Answer:

420 ways

Step-by-step explanation:

According to the given statement:

We want to divide the 10 dogs into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that fluffy is in the 3-dog group and nipper is in the 5-dog group.

In this way we have 8 dogs left.

2 spaces left in 3 dogs group

4 spaces left in 5 dogs group

and 2 spaces in 2 dogs group

Therefore:

= 8!/2!4!2!

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

= 8*7*6*5/2*2

= 1680/4

=420

It means there are 420 ways to from the groups....

Answer 2

Place Fluffy in the 3-dog group and Nipper in the 5-dog group. This leaves 8 dogs remaining to put in the last two spots of Fluffy's group, which can be done in 8C2 ways. Then there are 6 dogs remaining for the last 4 spots in Nipper's group, which can be done in 6C4. The remaining 2-dog group takes the last 2 dogs. So the total number of possibilities is 8C2x6C2=420