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In a spelling bee, scholarships are awarded to the top three spellers. The first-place speller receives $5,000, the second-place speller receives $3,000, and third place receives $2,000. Twelve students participate in the spelling bee.

Complete the sentences below.

The situation represents a __________.

There are __________ ways to award the prizes.

Answer :

Final answer:

The situation represents a combinatorial problem where there are 1,320 ways to award the scholarships to the top three spellers out of the twelve participants.

Explanation:

This situation represents a combinatorial problem in mathematics, specifically it's about calculating permutations. These permutations are important when determining the number of different ways we can award the scholarships to the top three spellers out of twelve participants. To calculate the number of ways to award the prizes, we use the permutation formula which is P(n, k) = n! / (n - k)!, where n is the total number of participants and k is the number of top positions. For the spelling bee example, this would be P(12, 3), which equals 12! / (12 - 3)! = 12 x 11 x 10 = 1,320 ways to award the prizes.

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Rewritten by : Jeany