In how many ways can three different balls be arranged in nine different boxes in a row such that the number of balls in each box does not exceed 1?Choices:- 504 502 506 510
Question
In how many ways can three different balls be arranged in nine different boxes in a row such that the number of balls in each box does not exceed 1?Choices:- 504 502 506 510
Solution
The problem can be solved in two steps:
Step 1: Choose 3 boxes out of 9 to place the balls. This can be done in 9C3 ways. The formula for combinations is nCr = n! / r!(n-r)!, where n is the total number of items, and r is the number of items to choose. So, 9C3 = 9! / 3!(9-3)! = 84 ways.
Step 2: Arrange the 3 balls in the chosen boxes. Since the balls are distinct, they can be arranged in 3! (3 factorial) ways, which is 321 = 6 ways.
So, the total number of ways to arrange the balls is the product of the number of ways to choose the boxes and the number of ways to arrange the balls in the chosen boxes, which is 84 * 6 = 504.
So, the answer is 504.
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