Question

At a competition with 7 runners, medals are awarded for first, second, and

Answer 1

Answer:

Option A - Permutation; number of ways = 210

Step-by-step explanation:

Given : At a competition with 7 runners, medals are awarded for first, second, and  third places. Each of the 3 medals is different.

To find : How many ways are there to  award the medals?        

Solution :

There are 7 runners but medals are three.

The first runner up got first medal as one is locked.

The second runner up got second medal as second is locked.

The third runner up got the third medal.

So, There is a permutation.

Number of ways to award the medals is $^7P_3$

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

Substitute the values,

$^7P_3=\frac{7!}{(7-3)!}$

$^7P_3=\frac{7\times 6\times 5\times 4!}{4!}$

$^7P_3=210$

Therefore, Option A is correct.

Permutation; number of ways = 210