Question

30 objects are to be divided into three groups containing 7, 10, 13 objects. Find the number of distinct ways of doing so.

Answer 1

First we can select 7 objects out of 30 for the first group in ³⁰C₇ ways.

Now there are 23 objects left out of which we can select 10 objects for the second group in ²³C₁₀ ways.

Remaining 13 objects can be selected for the third group in ⁵C₅ ways.

∴ Required number of ways = ³⁰C₇ x ²³C₁₀ x ¹³C₁₃