Question 1158935
<i><b>A)How many five person committees have 2 freshmen, 1 sophomore, and 2 seniors?</i></b>
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10C2 * 3C1 * 8C2 = {{{(10!/(2!*8!)) * (3!/(1!*2!)) * (8!/(2!*6!))}}} = 45 * 3 * 28 = <b>3780</b>
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<i><b>B)How many five person committees have exactly 1 sophomore?</i></b>
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3C1 * 24C4 = {{{(3!/(1!*2!)) * (24!/(4!*20!))}}} = 3 * 10626 = <b>31878</b>
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<i><b>C)How many five person committees have at least 2 juniors?</i></b>
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(6C2 * 21C3) + (6C3 * 21C2) + (6C4 * 21C1) + 6C5 = {{{((6!/(2!*4!)) * (21!/(3!*18!))) + ((6!/(3!*3!)) * (21!/(2!*19!))) + ((6!/(4!*2!)) * (21!/(1!*20!))) + (6!/(5!*1!))}}} 
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= (15 * 1330) + (20 * 210) + (15 * 21) + 6 
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= 19950 + 4200 + 315 + 6 = <b>24471</b>