There are 5 people. (Ted, Barney, Lily, Marshal and Robin)
Also there were 4 blue French horns, 5 yellow Umbrellas and 6 Suits in a shop.
The number of ways to place $n$ indistinguishable balls into $k$ labelled urns is $\large \binom{n+k-1}{n} = \binom{n+k-1}{k-1}$
Number of ways to distribute 4 blue french horns among 5 people = $\large \binom{n+k-1}{k-1} = \binom{4+5-1}{5-1} = \binom{8}{4}$
Similarly number of ways to distribute 5 yellow Umbrellas = $\large \binom{9}{4}$
and number of ways to distribute 6 Suits = $\large \binom{10}{4}$
Total Number of ways to distribute all times = $\large \binom{8}{4} * \binom{9}{4} * \binom{10}{4}$