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An organisation has 2 departments Quant and English. There are 3 women and 2 men in Quant department while 2 women and 3 men in English department. In how many ways can a meeting of 4 people be conducted which should contain 2 men and 2 women and at the same time 2 of them should be of Quant Department and 2 from English Department.

An organisation has 2 departments Quant and English. There are 3 women and 2 men in Quant department while 2 women and 3 men in English department. In how many ways can a meeting of 4 people be conducted which should contain 2 men and 2 women and at the same time 2 of them should be of Quant Department and 2 from English Department. Correct Answer 46

The selection can be done in following ways:

2 men from Quant Department and 2 women from English Department

⇒ Number of ways = 2C2 × 2C2

⇒ 1 × 1 = 1

Or

2 women from Quant Department and 2 men from English Department

⇒ Number of ways = 3C2 × 3C2

⇒ 3 × 3 = 9

Or

1 woman and 1 man from Quant Department and 1 woman and 1 man from English Department

⇒ Number of ways = 3C1 × 2C1 × 3C1 × 2C1

⇒ 3 × 2 × 3 × 2 = 36

∴ Total number of ways = 1 + 9 + 36 = 46

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