Question

Thirteen different gifts have to be packed in thirteen gift boxes. There are 4 boxes that are too small for 8 of the gifts. Find the number of ways of packing the gifts in the gift boxes.

Answer 1

There are a total 13 non-identical gifts and gift boxes. Among them:

Large gifts = 8	Small gifts = 5
Large gift boxes = 9	Small gift boxes = 4

8 large gifts can be packed in 9 large gift boxes in ${}^9{p}_8=9!$ ways

5 small gifts can be packed in the remaining 5 boxes (4 small + 1 large) in 5! ways.

Hence, the number of ways of packing all the gifts =
$9!\times 5!=362,880\times 120=43,545,600$