# 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? - Mathematics

MCQ

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?

• 159

• 194

• 205

• 209

#### 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

Concept: Permutation and Combination (Entrance Exam)
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