Question

the number of ways bin which 7 boys sit in a round table so that two particular boys may sit together is
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Answer 1

Answer:

Name seven boys as A, B, C, D, E, F and G.

Now, a group of two boys can be chosen in (7C2) = 21 ways.

Now, each such ‘two-boy group’ can be arranged in 2 ways (say, ‘AE’ and ‘EA’).

Now, when these two boys will sit next to one another, they are to be treated as a single entity. So, virtually, it becomes a permutation of (7 -2 + 1) = 6 characters around a round table. For a round table, this can be done in (6 - 1)! = 5! = 120 ways.

Therefore, there are (21*2*120) = 5040 ways that seven boys can be seated at a round table so that any two boys are next to each other.

If it is a case of two particular boys instead of any two boys; the answer shall be in (2 * 120) ways = 240 ways.