Discussion

Explanation:

Here shirts are identical, and people are distinct.

We need to give at least 1 shirt to all 3. Let us give 1 shirt to each of the three, hence we will have 9 shirts left. Now there is not restriction on distribution these 9 shirts.

Let the each of three persons receive x, y and z number of shirts from these 9 shirts.

∴ x + y + z = 9.

Note: This is same as distributing n identical item to r different people. 

No. of ways of distributing n identical items to r distinct people = ^n+r-1C_r-1.

⇒ Number of ways 9 identical shirts can be given to 3 people such that each may / may not receive a shirt = ^9+3-1C_3-1 = ¹¹C₂ = 55 ways.

Hence, 55.

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