[209] In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can t

For Competitive Exams

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

Explanation:

We may have [1 boy and 3 girls] or [2 boys and 2 girls] or [3 boys and 1 girl] or [4 boys].

$\therefore$ Required number of ways	= (⁶C₁ x ⁴C₃) + (⁶C₂ x ⁴C₂) + (⁶C₃ x ⁴C₁) + (⁶C₄)
	= (⁶C₁ x ⁴C₁) + (⁶C₂ x ⁴C₂) + (⁶C₃ x ⁴C₁) + (⁶C₂)
	=$\left (6 \times 4\right)$ +$ \left(\dfrac{6 \times 5}{2 \times 1} \times\dfrac{4 \times 3}{2 \times 1} \right) $+$ \left(\dfrac{6 \times 5 \times 4}{3 \times 2 \times 1} \times 4\right) $+$ \left(\dfrac{6 \times 5}{2 \times 1} \right) $
	= (24 + 90 + 80 + 15)
	= 209.

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