Please help me with this problems. 5 people are selected from a group of 8 to re

Question

Please help me with this problems.

5 people are selected from a group of 8 to receive a prize. If the prizes are indistinguishable (you can't tell them apart), and each person can receive at most one prize, how many ways could the prizes be given? Same question, but now the prizes are distinguishable (you can tell them apart). Now suppose that 5 indistinguishable prizes will be distributed among 8 people. A winner can receive more than one prize. In how many ways could the 5 prizes be distributed?

Explanation / Answer

1) 8C5=1120 ways

2) 8*7*6*5*4=6720 ways

3) 8!/5!+8!/4!1!+8!/3!2!=336+1680+3360=5376 ways

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