A bag contains 7 blue coloured balls, 8 yellow coloured balls and 5 gr

1.	A bag contains 7 blue coloured balls, 8 yellow coloured balls and 5 green coloured balls. In how many ways can three balls be picked from the bag so that we get balls of exactly two different colours?1). 2732). 4693). 7594). 829
Answer» If three BALLS are PICKED, there can be balls of exactly two colours in the following cases: i) Two blue balls and one yellow ball This can be done in ⁷C₂ × ⁸C₁ways, i.e. 21 × 8 = 168 ways. ii) Two blue balls and one green ball This can be done in ⁷C₂ × ⁵C₁ways, i.e. 21 × 5 = 105 ways. iii) Two yellow balls and one blue ball This can be done in ⁸C₂ × ⁷C₁ways, i.e. 28 × 7 = 196 ways. iv) Two yellow balls and one green ball This can be done in ⁸C₂ × ⁵C₁ways, i.e. 28 × 5 = 140 ways. v) Two green balls and one blue ball This can be done in ⁵C₂ × ⁷C₁ways, i.e. 10 × 7 = 70 ways. vi) Two green balls and one yellow ball This can be done in ⁵C₂ × ⁸C₁ways, i.e. 10 × 8 = 80 ways. ∴ Total number of ways in which it can be done = 168 + 105 + 196 + 140 + 70 + 80 = 759.

A bag contains 7 blue coloured balls, 8 yellow coloured balls and 5 green coloured balls. In how many ways can three balls be picked from the bag so that we get balls of exactly two different colours?1). 2732). 4693). 7594). 829

Answer»

If three BALLS are PICKED, there can be balls of exactly two colours in the following cases:

i) Two blue balls and one yellow ball

This can be done in ⁷C₂ × ⁸C₁ways, i.e. 21 × 8 = 168 ways.

ii) Two blue balls and one green ball

This can be done in ⁷C₂ × ⁵C₁ways, i.e. 21 × 5 = 105 ways.

iii) Two yellow balls and one blue ball

This can be done in ⁸C₂ × ⁷C₁ways, i.e. 28 × 7 = 196 ways.

iv) Two yellow balls and one green ball

This can be done in ⁸C₂ × ⁵C₁ways, i.e. 28 × 5 = 140 ways.

v) Two green balls and one blue ball

This can be done in ⁵C₂ × ⁷C₁ways, i.e. 10 × 7 = 70 ways.

vi) Two green balls and one yellow ball

This can be done in ⁵C₂ × ⁸C₁ways, i.e. 10 × 8 = 80 ways.

∴ Total number of ways in which it can be done = 168 + 105 + 196 + 140 + 70 + 80 = 759.