A batch comprises of 4 red and 7 green uniform boys. Figure out the number of methods can a squad of 5 unit be picked if the squad has (i) at least one red and one green uniform boy (ii) at least 3 red uniform boys?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1)

Answer 1

Given:

The batch has 4 red and 7 green uniform boys.

The squad is of 5 boys.

Concept:

For part (i) - This can be done by picking (1 red and 4 green or 2 red and 3 green or 3 red and 2 green or 4 red and 1 green)

For part (ii) - This can be done by picking (3 red and 2 green or 4 red and 1 green)

Explanation:

Part (i) :

1 red and 4 green = \(^4C_1 \times ^7C_4\) = 140 ways

2 red and 3 green = \(^4C_2 \times ^7C_3\) = 210 ways

3 red and 2 green = \(^4C_3 \times ^7C_2\) = 84 ways

4 red and 1 green = \(^4C_4 \times ^7C_1\) = 7 ways

∴ Total ways = 140 + 210 + 84 + 7

= 441 ways

Part (ii) :

3 red and 2 green = \(^4C_3 \times ^7C_2\) = 84 ways

4 red and 1 green = \(^4C_4 \times ^7C_1\) = 7 ways

∴ Total ways = 84 + 7

= 91 ways