How many ways a committee of six persons from 10 persons can be chosen

1.	How many ways a committee of six persons from 10 persons can be chosen along with a chair person and a secretary?
Answer» Selecting a chair person from the 10 persons can be done in 10 ways After the selection of chair person only 9 persons are left out so selecting a secretary (from the remaining a persons) can be done in 9 ways. The remaining persons = 8 Totally we need to select 6 persons We have selected 2 persons. So we have to select 4 persons Selecting 4 from 8 can be done in ⁸C₄ ways ∴ Total number of selection = 10 x 9 x ⁸C₄ = (10 x 9 x 8 x 7 x 6 x 5)/(4 x 3 x 2 x 1) = 6300

How many ways a committee of six persons from 10 persons can be chosen along with a chair person and a secretary?

Answer»

Selecting a chair person from the 10 persons can be done in 10 ways

After the selection of chair person only 9 persons are left out so selecting a secretary (from the remaining a persons) can be done in 9 ways.

The remaining persons = 8

Totally we need to select 6 persons

We have selected 2 persons.

So we have to select 4 persons

Selecting 4 from 8 can be done in ⁸C₄ ways

∴ Total number of selection = 10 x 9 x ⁸C₄

= (10 x 9 x 8 x 7 x 6 x 5)/(4 x 3 x 2 x 1) = 6300