Question

Let's say you have 7 cats and 4 dogs in a house.

How many ways could I put 4 of them in a room together if I always want 2 dogs and 2 cats?

How many ways can I line them up 3 at a time?

Answer 1

(A) It is a combination problem because only selection is there, but no ordering.

Formula for selecting r items out of n is

Number of ways of selecting 2 dogs out of 4 =

Number of ways of selecting 2 cats out of 7 =

Total number of ways = (number of ways of selecting 2 dogs)*(number of ways of selecting 2 cats) =6*21 = 126 ways

(B) Total number of animals = 7 + 4 = 11

Number of ways of select the first animal in the line = 11 ways

now, we are left with 10 animals. So, number of ways of selecting the 2nd animal in line = 10 ways

now, we are left with 9 animals. So, number of ways of selecting the 3rd animal in line = 9 ways

Total number of selecting 3 animals at a time in a line = 11*10*9 = 990 ways