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Question 120
Four girls and three boys have to sit in a row of seven chairs. If the chairs at the ends are to be occupied by girls and at least two of the three boys are supposed to sit adjacent to each other, then in how many different ways can they occupy these chairs?
Solution
The question is asked for atleast two, but the answer is provided for three.
First, arrange two out of four girls in the last two positions in 4*3 ways. Now consider three boys as a unit and two unarranged girls as two units. Arranging these three units can be done in 3! ways. Again, those three boys can be arranged in 3! ways.
So, the answer is 432.
