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There were 4 blue french horns, 5 yellow Umbrellas and 6 Suits in a shop. Ted, Barney, Lily, Marshal and Robin came to the shop to buy the items. How many different results could have been recorded if all of the items were sold?

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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 = $\large  \binom{8}{4} *  \binom{9}{4} *  \binom{10}{4}$

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