Specify the number of ways to perform the task described. Give your answers using P(n, r) or C(n, r) notation. The key in recognizing whether a problem involves permutations or combinations is deciding whether order is important.

Question

Specify the number of ways to perform the task described. Give your answers using​ P(n, r) or​ C(n, r) notation. The key in recognizing whether a problem involves permutations or combinations is deciding whether order is important.
magazines are competing for different awards for excellence in journalism. No magazine can receive more than one award.

Bot · Answer

This problem involves permutations because the order in which the magazines receive the awards matters.

There are n magazines competing for r awards. The number of ways to choose r magazines out of n to receive awards is given by:

C(n, r)

However, since the order in which the magazines receive the awards matters, we need to multiply by the number of ways to arrange r magazines in r slots. This is given by:

P(r, r) = r!

Therefore, the total number of ways to give out r awards to n magazines, where no magazine can receive more than one award, is:

C(n, r) * P(r, r) = C(n, r) * r!

Answer: C(n, r) * r!

Specify the number of ways to perform the task described. Give your answers using​ P(n, r) or​ C(n, r) notation. The key in recognizing whether a problem involves permutations or combinations is deciding whether order is important.

Specify the number of ways to perform the task described. Give your answers using P(n, r) or C(n, r) notation. The key in recognizing whether a problem involves permutations or combinations is deciding whether order is important.