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19 May 2020, 23:19
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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:
95%
(hard)
Question Stats:
39% (02:27) correct
61%
(02:18)
wrong
based on 109
sessions
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In how many ways can four couples be seated around a circular table such that people of the same gender do not sit in adjacent positions and exactly one of the four couples sit in adjacent positions?
A.48
B.36
C.96
D.24
E.25
A.48
B.36
C.96
D.24
E.25
20 May 2020, 00:10
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MBADream786
Let us first place 4 ladies in 4 places. They can be arranged in (4-1)! or 3! ways ---- 6 ways
Now, there is a restriction on placements of husbands.( refer the sketch)
So, let us take the husband of A first, he can be placed in 2 places, and as no other can sit along with their other halves, there is only 1 way to arrange the remaining 3 husbands., so 2*1 way.
But, there are 4 husbands, so there are 4*2 ways.
Total 6*4*2=48 ways.
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General Discussion
20 May 2020, 00:06
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In how many ways can four couples be seated around a circular table such that people of the same gender do not sit in adjacent positions and exactly one of the four couples sit in adjacent positions?
A.48
B.36
C.96
D.24
E.25
Let, first we arrange men.
Number of ways of arranging 4 men on a circular table =3!
Now, women have to be seated in between the men in the gaps.
Only one couple can sit together.
so, no of ways of selecting this couple = 4C1=4
Then the selected woman has two places to sit besides his couple that is on the two sides of his man.
After the woman is seated, three places are left and no other couple can sit together so the three women will have only one option left.
Hence, the number of ways in which 4 couples be seated around a circular table such that people of same gender do not sit in adjacent positions and exactly one of the four couples sit in adjacent positions =3!× 4C1×2=6×4×2=48
correct answer A
A.48
B.36
C.96
D.24
E.25
Let, first we arrange men.
Number of ways of arranging 4 men on a circular table =3!
Now, women have to be seated in between the men in the gaps.
Only one couple can sit together.
so, no of ways of selecting this couple = 4C1=4
Then the selected woman has two places to sit besides his couple that is on the two sides of his man.
After the woman is seated, three places are left and no other couple can sit together so the three women will have only one option left.
Hence, the number of ways in which 4 couples be seated around a circular table such that people of same gender do not sit in adjacent positions and exactly one of the four couples sit in adjacent positions =3!× 4C1×2=6×4×2=48
correct answer A
