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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2009

  • question_answer
        7 relatives of a man comprises 4 ladies and 3 gentlemen his wife has also 7 relatives, 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of mans relative and 3 of the wifes relative?

    A)  485                                       

    B)  500

    C)  486                                       

    D)  102

    Correct Answer: A

    Solution :

                    The possible cases are Case I: A man invites 3 ladies and woman invites 3 gentlemen \[\Rightarrow \]               \[^{4}{{C}_{3}}{{.}^{4}}{{C}_{3}}=16\] Case II: A man invites (2 ladies, 1 gentleman) and women invites (2 gentlemen, 1 lady) \[\Rightarrow \]               \[{{(}^{4}}{{C}_{2}}{{.}^{3}}{{C}_{1}}).{{(}^{3}}{{C}_{1}}{{.}^{4}}{{C}_{2}})=324\] Case III: A man invites (1 lady, 2 gentlemen) and women invites (2 ladies, 1 gentleman) \[\Rightarrow \]               \[{{(}^{4}}{{C}_{1}}{{.}^{3}}{{C}_{2}}).{{(}^{3}}{{C}_{2}}{{.}^{4}}{{C}_{1}})=144\] Case IV: A man invites (3 gentlemen) and women invites (3 ladies) \[\Rightarrow \]               \[^{3}{{C}_{3}}{{.}^{3}}{{C}_{3}}=1\] \[\therefore \]Total number of ways \[=16+324+144+1=485\]


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