A committee of 11 members is to be formed from 8 males and 5 females. if m is the number of ways the commitee is formed with at least 6 males and n is the number of ways the commitee is formed with at least 3 females, then :

  • Option 1)

    m+n=68

  • Option 2)

    m=n=78

  • Option 3)

     n=m-8

  • Option 4)

    m=n=68

 

Answers (1)

m=\left ( 6M,5F \right )+\left ( 7M,4F \right )+\left ( 8M,3F \right )

       =^{8}C_{6}\times^{5} C_{5}+^{8}C_{7}\times^{5} C_{4}+^{8}C_{8}\times ^{5}C_{3}

          =78  

m=\left ( 3F,8M \right )+\left ( 4F,7M \right )+\left ( 5F,6M \right )

      =^{5}C3\times ^{8}C_{8}+^{5}C_{4}\times^{8} C_{7}+^{5}C_{3}\times^{8} C_{3}

      =78

m=n=78

 


Option 1)

m+n=68

Option 2)

m=n=78

Option 3)

 n=m-8

Option 4)

m=n=68

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