Question

Twenty-three student compete in a math competition in which the top three studentsare recognized with trophies for first, second, and third place. How many different outcomes arethere for the top three places?

Answer 1

Answer:

10626 ways

Step-by-step explanation:

Given

Number of students = 23

Prizes = 3

Required

Number of different outcomes for the top 3

This question will be solved using permutation formula because it implies selection of 3 students from 23

$^nP_r = \frac{n!}{(n-r)!}$

Where n = 23 and r = 3

The formula becomes

$^{23}P_3 = \frac{23!}{(23-3)!}$

$^{23}P_3 = \frac{23!}{(20)!}$

$^{23}P_3 = \frac{23!}{20!}$

$^{23}P_3 = \frac{23 * 22 * 21 * 20!}{20!}$

$^{23}P_3 = 23 * 22 * 21$

$^{23}P_3 = 10626$

Hence, there are 10626 ways