Question

In the Olympics, there are 7 swimmers in the final race. How many ways can the gold,silver,and bronze medals be distributed among the 7 contestants?

Answer 1

Solution:

Following information has been provided:

The number of swimmers in the final race of the Olympic swimming competition =7

The counting rule will be used to find the number of ways.

Counting Rule: Counting Rule is a method used in probability to find the number of outcomes. If one operation can be done in n₁ ways and a second operation can be done in n₂ ways then the number of ways of doing both is n₁.n₂ .Similarly , this principle can be used for more than two operations.

Number of ways by which the gold medals can be distributed amongst the 7 contestants=7

Number of ways by which the silver medals can be distributed amongst the 7 contestants=6

(Except for those who awarded with gold).

Number of ways by which the bronze medals can be distributed amongst the 7 contestants=5

(Except for those who awarded with gold and silver).

By using the counting principle, the number of ways =7×6×5

                                                                                     =210

The total number of ways by which the gold, silver and bronze medals can be distributed among the 7 contestants is 210.

The total number of ways by which the gold, silver and bronze medals can be distributed among the 7 contestants is 210.