Four cats and five mice enter a race. In how many ways can they finish with a mouse placing first, second, and third

7200 ways

Step-by-step explanation:

Four cats and five mice enter a race. In how many ways can they finish with a mouse placing first, second, and third

Since order is important, we use combination rule

The mouse has to come First, Second and Third hence,

= C(n, r) = nCr = 5C3

3 mice coming 1st, Second and Third =

3! × 5C3

= 3! × 5!/3!(5 - 3)!

= 3! × 5!/3! × 2!

= 3! × 10

Then we have left 4 cats and 2 mice

= (4 + 2)!

= 6 !

Hence,

= 3! × 10 × 6!

= 7200 ways