In: Statistics and Probability
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?
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.