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ajaygaur319
Joined: 05 May 2019
Last visit: 01 Jan 2021
Posts: 125
Given Kudos: 143
Location: India
Schools: NYU Tech MBA "21
08 May 2020, 20:47
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (02:09) correct
45%
(02:28)
wrong
based on 512
sessions
History
Date
Time
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Not Attempted Yet
A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a choir be formed if both siblings cannot be selected together?
(A) 360
(B) 720
(C) 1120
(D) 2400
(E) 26880
(A) 360
(B) 720
(C) 1120
(D) 2400
(E) 26880
08 May 2020, 21:45
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ajaygaur319
Method-1
We need 4 siblings who must come from 4different sibling pairs therefore
Step-1: Select 4 sibling pairs = 8C4 ways = 70
Step-2: Select one child from each selected sibling pair = 2*2*2*2 = 16 ways
Total ways = 70*16 = 1120
Answer: Option C
Method-2
First sibling may be chosen in 16 ways
Second child may be chosen in 14 ways (leaving the selected child and his/her sibling)
Third child may be chosen in 12 ways (leaving the selected children and their siblings)
FOurth child may be chosen in 10 ways (leaving the selected children and their siblings)
Total Ways of making groups = 16*14*12*10
But this includes arrangement cause second child could come as first selection or vice versa so we need to exclude teh arrangements of 4 children from result
Required selection = 16*14*12*10 / 4! = 1120
Answer: Option C
General Discussion
Updated on: 09 May 2020, 08:05
Originally posted by Archit3110 on 09 May 2020, 05:20.
Last edited by Archit3110 on 09 May 2020, 08:05, edited 1 time in total.
Last edited by Archit3110 on 09 May 2020, 08:05, edited 1 time in total.
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all are boys ; 8c4 = 70
all are girls ; 8c4 = 70
3 boys 1 girl ; 8c3*5c1 =56*5 ; 280
1 boy 3 girls ; 8c1*7c3 = 8*35 ; 280
2 boys 2 girls ; 8c2*6c2 = 420
total 70+70+280+280+420 ; 1120
OPTION C
A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a choir be formed if both siblings cannot be selected together?
(A) 360
(B) 720
(C) 1120
(D) 2400
(E) 26880
all are girls ; 8c4 = 70
3 boys 1 girl ; 8c3*5c1 =56*5 ; 280
1 boy 3 girls ; 8c1*7c3 = 8*35 ; 280
2 boys 2 girls ; 8c2*6c2 = 420
total 70+70+280+280+420 ; 1120
OPTION C
A singing choir of 4 children is to be formed. The selection pool consists of 8 siblings pairs. In how many ways can a choir be formed if both siblings cannot be selected together?
(A) 360
(B) 720
(C) 1120
(D) 2400
(E) 26880
09 May 2020, 07:04
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Bookmarks
Archit3110
Check your mistakes
Method-3
case 1 ;
all are boys ; 8c4 = 70
all are girls ; 8c4 = 70
3 boys 1 girl ; 8c3*5c1 = 56*5 = 280 (Select girl such that she is not sibling of any chosen boy)
1 boy 3 girls ; 8c1*7c3 =8*35 = 280 (Select girls such that they are not sibling of chosen boy)
2 boys 2 girls ; 8c2*6c2 = 420
Total = 70+70+280+280+420 = 1120
Method-4
case 2 ;
total possible cases - ( set of siblings)
16c4- (8c2) - (8C1*(14*12/2)) = 1820 - 28 - (8*84) = 1820 - 28 - 672 = 1120
8C2 = selecting 2 sibling pairs out of 8 sibling pairs
8C1 = selecting 1 sibling pair out of 8 sibling pairs
(14*12/2) - Selecting 2 out of 14 such that they are not sibling pairs so 14 ways to choose 1st and 12 ways to choose second leaving chosen person and his cousin and then divided by 2 in order to exclude all arrangements of those two chose
Archit3110
