Question

Five prizes are to be given to five different people in a group of nineteen. In how many ways can a first prize, a second prize, a third prize and two fourth prizes be given?

Answer 1

The number of ways the prizes can be given is 1,200.

Step-by-step explanation:

To determine the number of ways the prizes can be given, we need to consider the different positions for each prize and the number of choices available for each position.

1. The first prize can be given to any one of the five people.
2. The second prize can be given to any one of the remaining four people.
3. The third prize can be given to any one of the remaining three people.
4. For the two fourth prizes, we have a total of two positions to fill with five remaining people, giving us 5 choices for the first fourth prize and 4 choices for the second fourth prize.

Therefore, the total number of ways the prizes can be given is: 5 x 4 x 3 x 5 x 4 = 1,200.