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How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes?

How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes? Correct Answer 40320

Now the first student is eligible to receive any of the 8 available prizes (so 8 ways), the second student will receive a prize from rest 7 available prizes (so 7 ways), the third student will receive his prize from the rest 6 prizes available(so 6 ways) and so on. So total ways would be 8! = 8*7*6*5*4*3*2*1 = 40320. Hence, the 7 prizes can be distributed in 40320 ways.

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