Question:
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each.
First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each.
First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is
Updated On: Jun 14, 2022
- $^6C_3 \, \times \, ^4C_2$
- $^4P_2 \, \times \, ^4P_3$
- $^4C_2 \, \times \, ^4P_3$
- None of these
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The Correct Option is D
Solution and Explanation
Since, the first 2 women select the chairs amongst 1 to 4 in ways. Now, from the remaining 6 chairs, three men could be arranged in
Total number of arrangements = $^4P_2 \, \times \, ^6P_3$
Total number of arrangements = $^4P_2 \, \times \, ^6P_3$
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
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- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
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