Question:
In how many ways a committee consisting of $3$ men and $2$ women, can be chosen from $7$ men and $5$ women?
In how many ways a committee consisting of $3$ men and $2$ women, can be chosen from $7$ men and $5$ women?
Updated On: Jul 6, 2022
- $45$
- $350$
- $4200$
- $230$
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The Correct Option is B
Solution and Explanation
Out of $7$ men, $3$ men can be chosen in $^{7}C_{3}$ ways and out of $5$ women, $2$ women can be chosen in $^{5}C_{2}$ ways. Hence, the committee can be chosen in $^{7}C_{3} \times\, ^{5}C_{2} = 350$ ways.
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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.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.