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.
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!
To determine the number of ways to perform the task described, we need to consider whether order is important or not.
Since no magazine can receive more than one award, the order in which the magazines receive the awards is important. Therefore, we are dealing with permutations.
Let's assume there are n magazines and r awards to be given.
The number of ways to select r magazines out of n, without considering the order, can be calculated using combinations formula C(n, r).
C(n, r) = n! / (r!(n - r)!)
However, since the order of the awards is important, we need to multiply the combination result by the number of ways to arrange the r awards among themselves, which is equivalent to the number of permutations of r items.
Therefore, the number of ways to perform the task described is given by P(n, r) = C(n, r) * r!
P(n, r) = (n! / (r!(n - r)!)) * r!