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Mugdho
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In a class of 10 students, in how many ways can you form a a 15 Jan 2022, 00:37
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C
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65% (hard)

Question Stats:

60% (02:41) correct 40% (02:23) wrong based on 136 sessions

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In a class of 10 students, in how many ways can you form a academic committee, if the committee must contain a minimum of 2 students ?

A. 1024
B. 1023
C. 1013
D. 1010
E. 90
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C
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Schools: IIM (A) ISB '24
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In a class of 10 students, in how many ways can you form a a 15 Jan 2022, 00:47
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Mugdho
In a class of 10 students, in how many ways can you form a academic committee, if the committee must contain a minimum of 2 students ?

a) 1024
b) 1023
c) 1013
d) 1010

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Every member has a choice to be chosen in committee or not being chosen in committee i.e. 2 choices
Hence, Total ways of making committee of any number of members from 0 to 10 \(= 2*2*2*2*2*2*2*2*2*2 = 2^{10} = 1024\)

But this 1024 includes cases in which committe may have 0 or 1 member (undesired cases) too

Total ways of taking 0 members = 1
Total ways of making committee of.1 member =\( ^{10}C_1 = 10\)

i.e. Total possible committee = 1024 - 1 - 10 = 1013

Answer: Option C
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In a class of 10 students, in how many ways can you form a a 24 Feb 2025, 18:14
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Wouldn't a committee of different students be distinct? For example would there not be 90 ways to make a committee of two people? 10 options for the first person and 9 for the second? I'm confused on that
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Mugdho
In a class of 10 students, in how many ways can you form a academic committee, if the committee must contain a minimum of 2 students ?

a) 1024
b) 1023
c) 1013
d) 1010

Posted from my mobile device


Every member has a choice to be chosen in committee or not being chosen in committee i.e. 2 choices
Hence, Total ways of making committee of any number of members from 0 to 10 \(= 2*2*2*2*2*2*2*2*2*2 = 2^{10} = 1024\)

But this 1024 includes cases in which committe may have 0 or 1 member (undesired cases) too

Total ways of taking 0 members = 1
Total ways of making committee of.1 member =\( ^{10}C_1 = 10\)

i.e. Total possible committee = 1024 - 1 - 10 = 1013

Answer: Option C
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In a class of 10 students, in how many ways can you form a a 25 Feb 2025, 00:09
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Kroliver4
Wouldn't a committee of different students be distinct? For example would there not be 90 ways to make a committee of two people? 10 options for the first person and 9 for the second? I'm confused on that
GMATinsight
Mugdho
In a class of 10 students, in how many ways can you form a academic committee, if the committee must contain a minimum of 2 students ?

a) 1024
b) 1023
c) 1013
d) 1010

Posted from my mobile device


Every member has a choice to be chosen in committee or not being chosen in committee i.e. 2 choices
Hence, Total ways of making committee of any number of members from 0 to 10 \(= 2*2*2*2*2*2*2*2*2*2 = 2^{10} = 1024\)

But this 1024 includes cases in which committe may have 0 or 1 member (undesired cases) too

Total ways of taking 0 members = 1
Total ways of making committee of.1 member =\( ^{10}C_1 = 10\)

i.e. Total possible committee = 1024 - 1 - 10 = 1013

Answer: Option C
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We need committees with a minimum of 2 students, not exactly 2. Review the solution with this in mind.
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