Question:
Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is :
Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is :
Updated On: Feb 14, 2025
- 200
- 300
- 500
- 350
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The Correct Option is B
Solution and Explanation
Required number of ways
= Total number of ways - When $A$ and $B$ are always included.
$ = {^5C_2} . {^7C_3} - {^5C_1} {^5C_2} = 300 $
= Total number of ways - When $A$ and $B$ are always included.
$ = {^5C_2} . {^7C_3} - {^5C_1} {^5C_2} = 300 $
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Permutations and Combinations
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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.
- 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.