Question 128

3 Girls and 4 boys are to be seated in a row on 7 chairs in such a way that all the three girls always sit together. In how many different ways can it be done ?

Solution

Total number of persons = 3 + 4 = 7

The girls always sit together.

Considering the three girls as 1 person, we have 5 persons which can be arranged in 5! ways

But corresponding to each way of these arrangements, the girls can be arranged together in 3! ways.

Hence, required number of words = $$5! \times 3!$$

= 120 * 6 = 720

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