Question

In how many ways can 18 objects be divided into 3 groups containing 9, 6, 3 objects respectively?

Answer 1

Answer:

¹⁸C₉*⁹C₆/6

Step-by-step explanation:

Hi,

Given 18 objects, let me assume all objects are  distinct,

Let 3 different groups be labelled as X, Y and Z

Let us choose 9 objects for group X, which can be done in ¹⁸C₉ ways

Let us chose 6 objects for group Y from the remaining 9 objects

which can be done in ⁹C₆ ways and the rest in the group Z

But , since the order of the group in which we fix X, Y  and Z is

immaterial all the permutations of X, Y and Z which could be

done in 3! ways result in the same combination, we need to

divide by 3!

Total number of ways all of 18 objects be distributed

are ¹⁸C₉*⁹C₆/6.

Hope, it helps !