A running race is conducted between $10$ boys.the first three winners gets Gold medal,Silver medal and bronze medal respectively,in how many ways can we the three winners?

27

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1000

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30

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720

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Solution

The correct option is D $720$
Assume a boy gets a gold medal.
Any one of the ten can get a gold medal.
Then the second winner will get a silver.
And the third will win a bronze.
At first, any of the tens can win a gold.
Thus, any $9$ of them are now applicable to win a silver.
This leaves the bronze to have any one of the $8$ .
So, the total number of ways to do this becomes
$10 \times 9 \times 8 = 720$ ways.

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A running race is conducted between 10 boys.the first three winners gets Gold medal,Silver medal and bronze medal respectively,in how many ways can we the three winners?

A running race is conducted between $10$ boys.the first three winners gets Gold medal,Silver medal and bronze medal respectively,in how many ways can we the three winners?