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Question

# In how many ways can 4 different prizes be given to any 4 of 10 people if no person receives more than 1 prize?

Solution

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First prize can be given to anyone of 10 people. Then, second prize can be given to anyone of 9 people remaining, and so on...

By the multiplication principle, the number of ways that 4 different prizes can be given to any 4 of 10 people is:

$10\cdot 9\cdot 8\cdot 7=5040$

$\textbf{The multiplication principle}$

If an action can be performed in $n_1$ ways, and for each of these ways another action can be performed in $n_2$ ways, then the two actions can be performed together in $n_1n_2$ ways.

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