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

Answer:

C 600

Step-by-step 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

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

Now out of 25 , 1 got the first place

So, n =25

r =1

$^{25}C_1 = \frac{25!}{1!(25-1)!}$

$^{25}C_1 = \frac{25!}{1!(24)!}$

$^{25}C_1 =25$

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

So, n = 24

r = 1

$^{24}C_1 = \frac{24!}{1!(24-1)!}$

$^{24}C_1 = \frac{24!}{1!(23)!}$

$^{24}C_1 =24$

So, no. of ways they can finish in first and second place = $^{25}C_1 \times ^{24}C_1$

                                                                                             = $25\times 24$

                                                                                             = $600$

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