Question

A boy finally got the 11 autographed shirts, each for his favorite player, from his love team. The shirts will be individually framed and hung on the walls of your room. If you will hang 4 shirts on one wall, 4 on another wall, and 3 on a third wall, in how many ways can you hang your shirts if the order between shirts on each wall matters?

Answer with 4 decimals.

Answer 1

There are 3 walls.

Lets consider the 1st wall. 4 shirts can be hung on it. The number of ways to pick these 4 shirts out of 11 is ¹¹C₄.

The number of ways of arranging these 4 shirts on 1st wall = 4! * ¹¹C_4.

Lets consider the 2nd wall. 4 shirts can be hung on it. 4 shirts have already been picked for the 1st wall so the remaining number of shirts = 11 - 4 = 7. The number of ways to pick 4 shirts out of these 7 is ⁷C₄.

The number of ways of arranging these 4 shirts on 2nd wall = 4! * ⁷C_4.

Now consider the 3rd wall. 8 shirts have already been picked for the previous 2 walls. So the remianing 3 shirts oit of 11 would have to hung on this wall. The number of ways of arranging these 3 shirts on this wall = 3! * 1_.

_{Hence, the number of ways in which 11 shirts can be hung on these 3 walls =} The number of ways of arranging first 4 shirts on 1st wall * The number of ways of arranging next 4 shirts on 2nd wall * The number of ways of arranging remaining 3 shirts on 3rd wall = (4! * ¹¹C₄) _* (4! * ⁷C₄) _* (3! * 1) = 24*330 * 24*35 * 6 = 39916800