From a group of $$6$$ boys and $$6$$ girls a volleyball team of $$6$$ players is to be selected. What is the probability

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From a group of $$6$$ boys and $$6$$ girls a volleyball team of $$6$$ players is to be selected. What is the probability

by AAPL » Thu Feb 08, 2024 5:14 pm

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From a group of $$6$$ boys and $$6$$ girls a volleyball team of $$6$$ players is to be selected. What is the probability that the team consists of $$4$$ boys and $$2$$ girls?

A. $$\dfrac{5}{33}$$
B. $$\dfrac{225}{308}$$
C. $$\dfrac{5}{22}$$
D. $$\dfrac{225}{311}$$
E. $$\dfrac{75}{308}$$

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Re: From a group of $$6$$ boys and $$6$$ girls a volleyball team of $$6$$ players is to be selected. What is the probabi

by mapadvantageprep » Fri Feb 16, 2024 9:48 am
To find the probability that the volleyball team consists of 4 boys and 2 girls, we need to consider the total number of ways to select 4 boys from the group of 6 boys and 2 girls from the group of 6 girls, divided by the total number of ways to select 6 players from the combined group of boys and girls.

Total number of ways to select 4 boys from group of 6 = 6C4 = 15
Total number of ways to select 2 girls from group of 6 = 6C2 = 15
Total number of ways to select 6 players from group of 12 = 12C6 = 924

The probability that the team consists of 4 boys AND 2 girls
= (15 x 15) / 924
= 75/308