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There are 6 people in a raffle drawing. Two raffle winners each win gift cards. Each gift card is the same. How many ways are there to choose the winners?Decide if the situation involves a permutation or a combination, and then find the number of ways to choose the winners.A.Permutation; number of ways = 15B.Permutation; number of ways = 30C.Combination; number of ways = 15D.Combination; number of ways = 30SUBMITarrow_backPREVIOUS

Question

There are 6 people in a raffle drawing. Two raffle winners each win gift cards. Each gift card is the same. How many ways are there to choose the winners?Decide if the situation involves a permutation or a combination, and then find the number of ways to choose the winners.A.Permutation; number of ways = 15B.Permutation; number of ways = 30C.Combination; number of ways = 15D.Combination; number of ways = 30SUBMITarrow_backPREVIOUS

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Solution

This situation involves a combination, not a permutation, because the order in which the winners are chosen does not matter.

In a combination, the order of selection does not matter, while in a permutation, the order is important. Here, it doesn't matter who is chosen first or second for the gift cards, just that two people are chosen.

The formula for combinations is C(n, r) = n! / [r!(n - r)!], where n is the total number of options, r is the number of options chosen, and "!" denotes a factorial.

Here, n = 6 (the number of people in the raffle) and r = 2 (the number of winners).

So, the number of ways to choose the winners is C(6, 2) = 6! / [2!(6 - 2)!] = (65) / (21) = 15.

So, the answer is C. Combination; number of ways = 15.

This problem has been solved

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