Picking r objects from n when order counts

Question

In how many different ways can 10 pigeons roost in 15 pigeon holes, if pigeons like to sleep alone?

Answer 1

You wish to choose 10 pigeon holes out of 15 in order.

The answer to both is ₁₅P₁₀=15!/5!=

Andre W.s answer correct, order counts.

3003×10!=10897286400.

Apologies.

Answer 2

The first pigeon has 15 choices, the second pigeon has 14 choices etc, down to the 10th pigeon which still has 6 choices. Therefore, the total is

 

15*14*...*6 = 15!/5! ≈ 1.09*10¹⁰ permutations.