Answer:
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
