You and your friend enter a drawing with 3 different prizes. A total of 7 people
entered the drawing, and prizes are awarded randomly
There are 210 ways to award the prizes
What is the probability that you win first prize and your friend wins second
prize?

The probability that you win first prize and your friend wins second

prize is 5/210

Step-by-step explanation:

Step 1 :

Total number of prizes awarded = 3

Number of people entering the draw = 7

Number of ways to award the prize = 210

We need to find the probability that we win the first and the second prize

Step 2 :

Out of the 3 prizes we need the first and the second. Hence the prize for the first and the second positions are fixed as we do not consider the remaining 5 people to win the prize here.

Hence the remaining number of people who can win the 3rd prize  = 5

The number of ways one of them wins the 3rd prize  = 5

The total number of ways = 210

Hence the probability of the first 2 prizes fixed and the remaining 3rd awarded to the rest of the 5 people is 5/210

Step 3 :

The required probability 5/210