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From a group of 10 boys and 12 girls, a committee of 4 students is chosen at random.


What is the probability of that all 4 members of the committee will be boys?


What is the probability of that all 4 members of the committee will be girls?


What is the probability there will be a least 1 girl on the committee?

Verified Answer :

LammettHash

All 4 members are boys: \(\dfrac{\binom{10}4\binom{12}0}{\binom{22}4}=\dfrac6{209}\)

All 4 members are girls: \(\dfrac{\binom{10}0\binom{12}4}{\binom{22}4}=\dfrac9{133}\)

At least 1 girl: this outcome is complementary to the event that the committee consists of all boys, so this probability is \(1-\dfrac6{209}=\dfrac{203}{209}\).

If you're not familiar with the notation,

\(\dbinom nk=\dfrac{n!}{k!(n-k)!}\)

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