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There are 6 teachers of whom two are from Science, 2 from Arts and the remaining, two from Commerce. They have to stand in a line so that the 1 two Science teachers, two arts teachers and also the two Commerce teachers are together. Find the number of ways in which they can do so:

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Solution

Treat them as 3 units which can be arranged, in 3! = 6 ways. The two persons corresponding to each of these can be arranged in 2! = 2 ways each. Hence the total number is 6 x 2 x 2 x 2 - 48.

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