Question

Seven runners are competing in a race where 3 of them will earn medals for finishing first, second, and third. How many possible ways can the medals be awarded among the seven runners?

a) 7
b) 21
c) 35
d) 42

Answer 1

The number of possible ways the medals can be awarded among the seven runners is 35.

Step-by-step explanation:

The number of possible ways the medals can be awarded among the seven runners can be found using combinations. Since there are 3 medals to be awarded among the 7 runners, we can use the formula for combinations:

C(n, r) = n! / (r!(n - r)!)

Plugging in the values, we have:

C(7, 3) = 7! / (3!(7 - 3)!)

Simplifying the expression, we get:

C(7, 3) = 7! / (3! * 4!)

Calculating the factorials:

C(7, 3) = 7 * 6 * 5 / (3 * 2 * 1)

C(7, 3) = 35

Therefore, there are 35 possible ways the medals can be awarded among the seven runners.