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Source: Manhattan Prep
The students at Natural High School sell coupon books to raise money for after-school programs. At the end of the coupon sell, the school selects six to win prizes as follows:
From the homeroom with the highest total coupon-book sales, the students with the first-, second-, and third-highest sales receive $50, $30, and $20, respectively; from the homeroom with the second-highest total coupon-book sales, the three-highest selling students receive $10 each. If Natural High School has ten different homerooms with eight students each, in how many different ways could the six prizes be awarded? (Assume that there are no ties, either among students or among homerooms)
A. \((2^7)(3^2)(5)(7^2)\)
B. \((2^8)(3^3)(5)(7^2)\)
C. \((2^9)(3)(5^2)(7^2)\)
D. \((2^9)(3^4)(5)(7^2)\)
E. \((2^8)(3^5)(5)(7^2)\)
The OA is B
The students at Natural High School sell coupon books to raise money for after-school programs. At the end of the coupon sell, the school selects six to win prizes as follows:
From the homeroom with the highest total coupon-book sales, the students with the first-, second-, and third-highest sales receive $50, $30, and $20, respectively; from the homeroom with the second-highest total coupon-book sales, the three-highest selling students receive $10 each. If Natural High School has ten different homerooms with eight students each, in how many different ways could the six prizes be awarded? (Assume that there are no ties, either among students or among homerooms)
A. \((2^7)(3^2)(5)(7^2)\)
B. \((2^8)(3^3)(5)(7^2)\)
C. \((2^9)(3)(5^2)(7^2)\)
D. \((2^9)(3^4)(5)(7^2)\)
E. \((2^8)(3^5)(5)(7^2)\)
The OA is B
