ACT Math Practice Question #1203 (Hard (33)) | Test Citadel
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ACT Math Difficulty: Hard (33)

Digital ACT Math Practice Question #1203

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A committee of $4$ students is to be randomly selected from a pool of $7$ seniors and $5$ juniors. What is the probability that the committee contains exactly $2$ seniors and $2$ juniors?
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Favorable = $\binom{7}{2}\binom{5}{2} = 21 \times 10 = 210$. Total = $\binom{12}{4} = 495$. Divide both by $15$: $210/15 = 14$, $495/15 = 33$. Directly yields $14/33$.

Masterclass Solution & Distractor Trap Analysis

The total number of ways to choose $4$ students from $12$ is $\binom{12}{4} = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = 495$. The number of ways to choose $2$ seniors from $7$ is $\binom{7}{2} = \frac{7 \times 6...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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