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Question:-Nine chairs are numbered 1 to 9. Three women and four men wish to occupy one chair each. First the women chose the chairs from amongst the chair marked 1 to 5; and then the men select the chairs from amongst the remaining. The number of possible arrangements isChoices:- 5C3 × 4C2 5C2 × 4P3 5C3 × 6C4 None of these

Question

Question:-Nine chairs are numbered 1 to 9. Three women and four men wish to occupy one chair each. First the women chose the chairs from amongst the chair marked 1 to 5; and then the men select the chairs from amongst the remaining. The number of possible arrangements isChoices:- 5C3 × 4C2 5C2 × 4P3 5C3 × 6C4 None of these

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Solution

The solution to this problem involves the use of combinations.

Step 1: The women have 5 chairs to choose from and they need to occupy 3 chairs. The number of ways this can be done is given by the combination formula 5C3.

Step 2: After the women have chosen their chairs, there are 6 chairs left (9 total chairs - 3 occupied by women = 6 remaining chairs). The men need to occupy 4 chairs from these remaining 6. The number of ways this can be done is given by the combination formula 6C4.

Step 3: The total number of possible arrangements is the product of the number of ways the women can choose their chairs and the number of ways the men can choose their chairs. This is given by 5C3 × 6C4.

So, the correct answer is "5C3 × 6C4".

This problem has been solved

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