Out of five girls and three boys, four children are to be randomly selected for a quiz contest. What is the probability that all the selected children are girls?

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Solution

The correct option is A
Total number of ways of selecting 4 children out of 8
= $8 C_{4} = \frac{8 \times 7 \times 6 \times 5}{1 \times 2 \times 3 \times 4} = 70$
Number of ways of selecting 4 girls out of 5 $= 5 C_{4} = 5$

Required probability = $\frac{5}{70} = \frac{1}{14}$

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Out of five girls and three boys, four children are to be randomly selected for a quiz contest. What is the probability that all the selected children are girls?

The correct option is A Total number of ways of selecting 4 children out of 8 = 8C4=8×7×6×51×2×3×4=70 Number of ways of selecting 4 girls out of 5 =5C4=5 Required probability = 570=114

The correct option is A
Total number of ways of selecting 4 children out of 8
= $8 C_{4} = \frac{8 \times 7 \times 6 \times 5}{1 \times 2 \times 3 \times 4} = 70$
Number of ways of selecting 4 girls out of 5 $= 5 C_{4} = 5$

Required probability = $\frac{5}{70} = \frac{1}{14}$