JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    There are three men and seven women taking a dance class. Number of different ways in which each man is paired with a woman partner, and the four remaining women are paired into two pairs each of two is

    A) 105

    B) 315

    C) 630

    D) 450

    Correct Answer: C

    Solution :

    [c] \[10<\begin{matrix}    3m  \\    7w  \\ \end{matrix}3\] Women can be selected in \[^{7}{{C}_{3}}\]ways and can be paired with 3 men in 3! Ways. Remaining 4 women can be grouped into two couples in \[4!/(2!\,\cdot 2!\,\,\cdot 2!)=3.\] Therefore, total \[{{=}^{7}}{{C}_{3}}\,.\,3!\,.\,3=630\].


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