Discussion

Explanation:

Here shirts are identical, and people are distinct.

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

The total number of shirts received is less than or equal to 12. Let’s say total number of shirts received is (12 – w).

∴ x + y + z ≤ 12 - w.

where, w ≥ 0.

⇒ x + y + z + w = 12.

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-1Cr-1.

∴ Required answer = ^12+4-1C_4-1 = ¹⁵C₃ = 455.

Hence, 455.

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