Question
In a group of 6 boys and 4 girls , four children are to be selected . In how many different ways can they be selected such that at least one boy should be there ?
Answer: Option D
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we may have (1 boy and 3 girls ) or ( 2 boys and 2 girls ) or ( 3 boys and 1 girls ) or(4 boys)
`:.` Required number of ways
= `(6_(C_ 1) xx 4_ (C_ 3)) + (6_ (C _ 2) xx 4_ (C _ 2)) + (6_ (C _3) xx 4_ (C _1)) + (6 _ (C _ 4))`
=`(6_(C_ 1) xx 4_ (C_ 1)) + (6_ (C _ 2) xx 4_ (C_ 2)) + (6_ (C _3) xx 4_ (C _1)) + (6 _ (C _ 2))`
= `(6 xx 4) + ((6 xx 5)/(2 xx 1) xx (4 xx 3)/(2 xx 1)) + ((6 xx 5 xx 4)/(3 xx 2 xx 1) xx 4) + ((6 xx 5)/(2 xx 1))`
= (24 + 90 + 80 + 15) = 209.
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