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How many two elements subsets from letters of english alphabet are the
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04 Aug 2023, 08:16
04 Aug 2023, 08:16
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How many two elements subsets from letters of english alphabet are there that do not contain the pair of d and z?
A. 162
B. 324
C. 649
D. 675
E. 972
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A. 162
B. 324
C. 649
D. 675
E. 972
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) Free Materials for the GRE General Exam - Where to get it!!
\(\Longrightarrow\) Best GRE Test Books of 2023
How many two elements subsets from letters of english alphabet are the
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08 Aug 2023, 02:23
08 Aug 2023, 02:23
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We need to select two element subsets from all the English alphabet (i.e., 26)
In case of set: (2,5) is same as (5,2).
Therefore, order of elements does not matter. Hence, we use combination instead of
permutation.
Number of ways to select 2 elements from 26, when order does not matter is 26C2.
According to the question, we do not want a subset that includes ๐ and ๐ง.
There will be only one subset containing ๐ and ๐ง, i.e. (๐, ๐ง).
So, requirement is all possible sets except the subset (๐, ๐ง).
โTotal subsets โ 1 =\( C^{26}_1\)
\(26!/2!(26-2)!=325\)
Total subset = 325-1=324
B is the answer
We need to select two element subsets from all the English alphabet (i.e., 26)
In case of set: (2,5) is same as (5,2).
Therefore, order of elements does not matter. Hence, we use combination instead of
permutation.
Number of ways to select 2 elements from 26, when order does not matter is 26C2.
According to the question, we do not want a subset that includes ๐ and ๐ง.
There will be only one subset containing ๐ and ๐ง, i.e. (๐, ๐ง).
So, requirement is all possible sets except the subset (๐, ๐ง).
โTotal subsets โ 1 =\( C^{26}_1\)
\(26!/2!(26-2)!=325\)
Total subset = 325-1=324
B is the answer
gmatclubot
How many two elements subsets from letters of english alphabet are the [#permalink]
08 Aug 2023, 02:23
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