Question

Find the number of ways of dividing 20 objects into three groups of sizes 8, 7, and 5.

Answer 1

First we can select 8 objects our of 20 for the first group in ²⁰C₈ways.

Now there are 12 objects left out of which we can select 7 objects for the second group in ¹²C₇ ways.

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

∴ Required number of ways = ²⁰C₈ × ¹²C₇ × ⁵C₅