Question

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

Answer 1

You answer is 25 times 24 which is 600. C

Answer 2

C 600

Explanation:

We are given that there are 25 people competing in a race.

We are required to find In how many ways can they finish in first and second place

We will use combination over here

`^nC_r = (n!)/(r!(n-r)!)`\

Now out of 25 , 1 got the first place

So, n =25

r =1

`^(25)C_1 = (25!)/(1!(25-1)!)`

`^(25)C_1 = (25!)/(1!(24)!)`

`^(25)C_1 =25`

Now since first place is occupied so for second place there are 24 people

So, n = 24

r = 1

`^(24)C_1 = (24!)/(1!(24-1)!)`

`^(24)C_1 = (24!)/(1!(23)!)`

`^(24)C_1 =24`

So, no. of ways they can finish in first and second place =
`^(25)C_1 * ^(24)C_1`

=
`25* 24`

=
`600`

Hence there are 600 ways so that they can finish in first and second place