JEE Main & Advanced Sample Paper JEE Main Sample Paper-42

  • question_answer
    Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is

    A) \[^{6}{{C}_{3}}{{\times }^{3}}{{C}_{2}}\]               

    B) \[^{4}{{P}_{2}}{{\times }^{4}}{{P}_{3}}\]

    C) \[^{4}{{C}_{2}}{{+}^{4}}{{P}_{3}}\]                       

    D)  None of these

    Correct Answer: D

    Solution :

    Since, first the 2 women select the chairs amongst 1 to 4. \[\therefore \]Number of ways \[{{=}^{4}}{{P}_{2}}\] Now, from the remaining 6 chairs three men could be arranged in \[^{6}{{P}_{3}}\] ways. \[\therefore \]Total number of arrangements \[{{=}^{4}}{{P}_{2}}{{\times }^{6}}{{P}_{3}}.\]


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