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  • In a race, there are 8 participants. In how many ways can the gold, silver, and bronze medals be awarded if the previous year's winner cannot win the gold medal again

In a race, there are 8 participants. In how many ways can the gold, silver, and bronze medals be awarded if the previous year's winner cannot win the gold medal again?

 

Option: 1

126 ways


Option: 2

420 ways


Option: 3

336 ways


Option: 4

720 ways


Answers (1)

best_answer

To solve this, we need to consider the different cases based on who wins the gold medal:

Case 1: If the previous year's winner does not win the gold medal:

There are 7 participants who can win the gold medal.

Once the gold medalist is determined, there are 7 remaining participants who can win the silver medal.

After the silver medalist is determined, there are 6 remaining participants who can win the bronze medal.

Therefore, the number of ways for this case is: 7 choices for the gold medal × 7 choices for the silver medal × 6 choices for the bronze medal = 294 ways.

Case 2: If the previous year's winner wins the gold medal again:

There is 1 participant who can win the gold medal (the previous year's winner).

Once the gold medalist is determined, there are 7 remaining participants who can win the silver medal.

After the silver medalist is determined, there are 6 remaining participants who can win the bronze medal.

Therefore, the number of ways for this case is: 1 choice for the gold medal × 7 choices for the silver medal × 6 choices for the bronze medal = 42 ways.

To find the total number of ways, we sum the possibilities for each case:

Total number of ways = 294 ways + 42 ways = 336 ways.

 

Posted by

Ritika Kankaria

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