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(D) To determine the number of ways the first $3$ prizes can be won by $10$ students,we use the concept of permutations because the order of winning m

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$720$

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(D) To determine the number of ways the first $3$ prizes can be won by $10$ students,we use the concept of permutations because the order of winning matters.The number of ways to arrange $r$ objects out of $n$ distinct objects is given by the formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 10$ and $r = 3$.Therefore,the number of ways is $^{10}P_3 = \frac{10!}{(10-3)!} = \frac{10!}{7!}$.Calculating this,we get $10 	imes 9 	imes 8 = 720$ ways.

Ten students are participating in a race. In how many ways can the first $3$ prizes be won?

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