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02 Dec 2024, 23:08
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E
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:
44% (01:38) correct
56%
(02:40)
wrong
based on 25
sessions
History
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Time
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A dance delegation of 4 people must be chosen from 5 pairs of dance partners. If 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?
A. 20
B. 30
C. 60
D. 70
E. 80
A. 20
B. 30
C. 60
D. 70
E. 80
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03 Dec 2024, 13:04
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sahil770
Let the \(5\) pairs be
\( m_1f_1, m_2f_2,m_3f_3,m_4f_4 \) and \(m_5f_5\)
Choosing males. From five males choose \(4\), this can be done in \(5\) ways or \(5_C_4\). e.g.
\(m_1, m_2 , m_3,m_4\)
\(m_1,m_2,m_3,m_5 \)
\(m_1,m_2,m_4,m_5 \)
\(m_1,m_3,m_4,m_5 \)
\(m_2,m_3,m_4,m_5 \)
Choosing females to pair with males. Now each of these males can choose any female except his partner. Thus each male has \(4\) options only.
\(m_1*4, m_2 *4, m_3*4,m_4*4 \)
\(m_1*4,m_2*4,m_3*4,m_5*4 \)
etc.
Thus \(16+16+16+16+16 = 80\)
Ans E
Hope it helped.
bhavyagmat
03 Dec 2024, 22:00
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Can someone point out the problem with the following solution
There are 5 pairs..Let us say AB,CD,EF,GH,IJ..
Now the condition say 2 dance partners cant be together..i.e A can be selected and his/her/its partner cant be selected subsequently...so A cant be with B, C cant be with D - so on and so forth.
We need to select 4 people from 5 pairs ( i.e 10 people)
Suppose I select the first individual
That I can do it in 10 differency ways( 10c1)
Then I want to select the second individual. 9 individuals left..We are barred from selecting the partner..So we are left with 8 people, and we select 1..(8C1)..
So it 10*8
Next we need to select 2 more people from balance 6 people ( 2 people have been selected and their respective partners are barred)
6C1 follows..His/Her/Its partner is barred..
We are left with 4 people..from whom 1 is to be selected...4c1
10*8*6*4 = 1920 should be the answer
There are 5 pairs..Let us say AB,CD,EF,GH,IJ..
Now the condition say 2 dance partners cant be together..i.e A can be selected and his/her/its partner cant be selected subsequently...so A cant be with B, C cant be with D - so on and so forth.
We need to select 4 people from 5 pairs ( i.e 10 people)
Suppose I select the first individual
That I can do it in 10 differency ways( 10c1)
Then I want to select the second individual. 9 individuals left..We are barred from selecting the partner..So we are left with 8 people, and we select 1..(8C1)..
So it 10*8
Next we need to select 2 more people from balance 6 people ( 2 people have been selected and their respective partners are barred)
6C1 follows..His/Her/Its partner is barred..
We are left with 4 people..from whom 1 is to be selected...4c1
10*8*6*4 = 1920 should be the answer
