There are 25 people competing in a race. In how many ways can they finish in first and second place? A 49 B 400 C 600 D 625

Mathematics · High School · Mon Jan 18 2021

llm

Answered on Sat Oct 15 2022

Formula :

nCr = n!/r!(n-r)!

Number of people, n = 25

First place winner, r = 1

So, 25C1 = 25!/1!(25-1)!

= 25 × 24!/24!

= 25

Now, remaining number of people = 25

Second place, r = 1

So,

24C1 = 24!/1!(24-1)!

= 24 × 23!/23!

= 24

So, Number of ways they can finish 1st and 2nd = 25 × 24

= 600

Hence, option (C) is correct.