1.

If `""^(m)C_(r)=0" for "rgtm` then the sum `sum_(r=0)^(m)""^(18)C_(r)""^(20)C_(m-r)` is maximum when m =A. 20B. 19C. 10D. 10

Answer» We have,
`sum_(r=0)^(m)""(18)C_(r)""^(20)xxC_(m-r)`
= Number of ways of choosing m persons out of 18 men and 20 women
`=""^(38)C_(m)`
Clearly, it is maximum when m =19.


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