Ten participants are participating in a competition. In how many ways can the first three prizes be won?Choices:- 920 620 720 850
Question
Ten participants are participating in a competition. In how many ways can the first three prizes be won?Choices:- 920 620 720 850
Solution
This is a permutation problem. The formula for permutations is P(n, r) = n! / (n-r)!. Here, n is the total number of participants (10) and r is the number of prizes (3).
Step 1: Calculate n! (10!) 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800
Step 2: Calculate (n-r)! (10-3)! 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Step 3: Substitute these values into the formula P(10, 3) = 3,628,800 / 5,040 = 720
So, the first three prizes can be won in 720 different ways. Therefore, the correct answer is 720.
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