Question

In how many ways can 7 identical red balls, 6 identical green balls, and 1 yellow ball be put in 14 distinct boxes such that each box contains only one ball?

___.

Answer 1

First, the only yellow ball can be placed in one of the 14 boxes in ${}^{14}$C${}_1$ = 14 ways.
Out of the remaining 13 boxes, we need to choose 6 places for the 6 identical green balls. This can be done in ${}^{13}$C${}_6$ ways.

Therefore, the total number of ways = 14 $\times$ ${}^{13}$C${}_6$ = 24024