Question

there are 22 participants in a spelling bee. in how many ways can the top 5 participants finish? use the formula for permutations to find your answer.

632,016
5,153,632
26,334
3,160,080

Explanation:

Identify the permutation parameters

$$ n = 22, \quad r = 5 $$

Apply the permutation formula

$$ P(n, r) = \frac{n!}{(n-r)!} $$

Calculate the final value

$$ P(22, 5) = \frac{22!}{17!} = 22 \times 21 \times 20 \times 19 \times 18 = 3,160,080 $$

Answer:

• (A) 632,016
• (B) 5,153,632
• (C) 26,334
• (D) 3,160,080 (Correct answer)