Question

Aidan has 6 (different) bulls and 10 (different) horses living at his animal sanctuary. He needs to place them in a line of 16 paddocks, and the bulls cannot be placed in adjacent paddocks (otherwise they will try to fight one another). How many ways can Aiden place the bulls and horses in the paddocks so that no two bulls are paddocks? [Hint: first arrange the horses, then consider possible places for the bulls.] in adjacent

Answer 1

Answer: 5225472000

Explanation:

Given : The number of bulls = 6

The number of horses = 10

Since Aidan needs to place them in a line of 16 paddocks, and the bulls cannot be placed in adjacent paddocks .

Also there are two ways to arrange the group pf bulls and horses.

Then , the number of ways Aiden can place the bulls and horses in the paddocks so that no two bulls are paddocks will be :_

`2*6!*10!=5225472000`

Hence, the number of ways Aiden can place the bulls and horses in the paddocks so that no two bulls are paddocks =5225472000