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29 Sep 2022, 01:14
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (02:13) correct
35%
(02:28)
wrong
based on 123
sessions
History
Date
Time
Result
Not Attempted Yet
A team of five people is to be formed from a pool of 5 professionals and 3 amateurs. The number of teams that can be formed such that the team contains at least 3 professionals is how many fewer than the total number of teams that can be formed (that is, teams formed with no mandatory conditions)?
(A) 10
(B) 11
(C) 26
(D) 46
(E) 56
(A) 10
(B) 11
(C) 26
(D) 46
(E) 56
29 Sep 2022, 04:28
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Bunuel
Solution:
- Total number of teams that can be formed = Choosing 5 from 8 choices \(= 8C5=56\)
- Total number of teams containing at least 3 professionals \(=30+15+1=46 \)
- 3 professionals AND 2 amateurs \(=5C3\times 3C2=10\times 3=30\)
- 4 professionals AND 1 amateur \(=5C4\times 3C1=5\times 3=15\)
- 5 professionals \(=5C5=1\)
- Thus, \(56-46=10\)
Hence the right answer is Option A
29 Sep 2022, 04:57
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no of ways in which 5 team can be formed without any condition is
8!/5!3!= 56 ways
now we have to form team containing atleast 3 professionals
lets find team with 3 amateurs and 2 professionals
let us say AAAPP
i.e 5!/3!2! = 10 ways
therefore team containing atleast 3 professionals
total ways - team with 3 amateurs and 2 professionals
56-10= 46 ways
now according to question
56-46= 10 ways
therefore correct option A
8!/5!3!= 56 ways
now we have to form team containing atleast 3 professionals
lets find team with 3 amateurs and 2 professionals
let us say AAAPP
i.e 5!/3!2! = 10 ways
therefore team containing atleast 3 professionals
total ways - team with 3 amateurs and 2 professionals
56-10= 46 ways
now according to question
56-46= 10 ways
therefore correct option A
