The students at Natural High School sell coupon books to raise money after-school programs. At the end of the coupon sale, the school selects six students 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, $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 student each, in how many different ways could the six prizes be awarded? (Assume that there are no ties, either among students or among homerooms.) Write your answer as a product of primes raised too various power ( do not actually compute the number).
OA is [spoiler](2^8)(3^3)(5)(7^2)[/spoiler]
OA is [spoiler](2^8)(3^3)(5)(7^2)[/spoiler]
Abdulla
