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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 ties are allowed, meaning multiple participants can receive th

In a race, there are 8 participants. In how many ways can the gold, silver, and bronze medals be awarded if ties are allowed, meaning multiple participants can receive the same medal?

 

Option: 1

4,096 ways


Option: 2

512 ways


Option: 3

1,024 ways


Option: 4

16,777,216 ways


Answers (1)

best_answer

For the gold medal, each of the 8 participants can either receive it or not, resulting in 2 choices for each participant. Therefore, there are \mathrm{2^8=256} possible combinations for the gold medal.

Similarly, for the silver medal, there are \mathrm{2^8=256} possible combinations.

And for the bronze medal, there are \mathrm{2^8=256} possible combinations as well.

To find the total number of ways, we multiply the number of combinations for each medal: 256 combinations for the gold medal × 256 combinations for the silver medal × 256 combinations for the bronze medal = 16,777,216 ways.




 

Posted by

Suraj Bhandari

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