Question:
The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman, is
The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman, is
Updated On: Jul 28, 2022
- $1960$
- $15!$
- $\left(15 !\right)^{2}$
- $14!$
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The Correct Option is B
Solution and Explanation
First team can be selected in $\left( \, ^{15} C_{1} . ^{15} C_{1}\right)$ way second in $\left(^{14} C_{1}\right)\left(^{14} C_{1}\right)$ way's and so on
So number of ways of selections $15$ teams $=\frac{\left(15 !\right)^{2}}{15 !}=\left(15 !\right)$
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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.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- 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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