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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?
Options
159
194
205
209
MCQ
Solution
209
Explanation:
We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
∴ Required number
= `(""^6C_1xx""^4C_3)+(""^6C_2xx""^4C_2)+(""^6C_3xx""^4C_1)+(""^6C_4)`
= `(6xx4)+((6xx5)/(2xx1)xx(4xx3)/(2xx1))+((6xx5xx4)/(3xx2xx1)xx4)+((6xx5)/(2xx1))`
= (24 + 90 + 80 + 15)
= 209
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Permutation and Combination (Entrance Exam)
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