Question:
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
Updated On: Jul 5, 2022
- $112$
- $140$
- $164$
- none of these
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The Correct Option is B
Solution and Explanation
Reqd. no of ways $=\,^{10}C_{6}-\,^{8}C_{4}=210-70
=140$
[$\because$ no. of ways in which two of the friends will attend the party $=\,^{8}C_{4}]$
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Notes on permutations and combinations
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.