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Question

Find the number of ways in which a lady can invite 6 guests selected from 10 friends so that two of the friends will not attend the party together ?.

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Solution

Let us consider that the two particular friends are A and B
If A is invited among six guests and B is not then, number of combinations to select 5 more guests from the remaining 8 friends will be
8C5=8!5!3!=56
If B is invited among the six guests and A is not then, number of ways of selecting the remaining guest will be
8C5=8!5!3!=56
Suppose both A and B are not included in the six guests then the number of such combinations will be
8C6=8!6!2!=28
Therefore total number of sets of guests that can be selected =56+56+28=140.

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