Question

one hundred twelve people bought raffle tickets to enter a random drawing for three prizes. how many ways can three names be drawn for first prize, second prize, and third prize?

Answer 1

There are 221,760 ways to draw three names for the first prize, second prize, and third prize in the raffle.

Step-by-step explanation:

The number of ways three names can be drawn for first prize, second prize, and third prize in the raffle can be calculated using the concept of combinations. Since there are 112 people and we want to select 3 names, we can use the formula for combinations, which is given by the expression nCr = n! / (r!(n-r)!), where n is the total number of people and r is the number of names we want to select.

Using this formula, we can calculate the number of ways as follows:

nCr = 112! / (3!(112-3)!) = (112*111*110) / (3*2*1) = 221,760

Therefore, there are 221,760 ways to draw three names for the first prize, second prize, and third prize in the raffle.

Answer 2

There are 1,367,120 different ways to draw three names for the prizes in the raffle from 112 people.

Step-by-step explanation:

The question inquires about the number of ways three names can be drawn for first, second, and third prizes from one hundred twelve people who bought raffle tickets. This is a permutation problem because the order in which the prizes are awarded matters.

To calculate the total number of permutations, we use the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!. In this case, n is 112 (the total number of people) and r is 3 (the number of prizes).

Thus, the number of ways to draw three names is:
112P3 = 112! / (112-3)! = 112! / 109! = 112 x 111 x 110.

Calculating the product, we find that there are 1,367,120 different ways to award the three prizes.