A lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of 5,

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 A lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of 5, given that two of the friends will not attend the party together is 

(a) 56 (b) 126 (c) 91 (d) 94 (e) None of these


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Salim Ahmed Kawsar

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(c) Number of ways of selecting 5 guests from nine friends = 9C5 Out of these, 7C3 ways are those in which two of the friends occur together [3 more persons to be selected out of remaining 7]
Number of ways, in which two of the friends will not attend the party together = 9C5 – 7C3 = 91.

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