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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?

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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?

(a) 40325

(b) 40320

(c) 40520

(d) 40720

The question was asked in final exam.

The above asked question is from Counting topic in section Counting of Discrete Mathematics

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The correct option is (b) 40320

The best I can explain: 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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