IPMAT 2022 - Quantitative Aptitude Question 15
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IPMAT 2022 - Quantitative Aptitude
Total Arrangements where Mr & Mrs Sharma together & Mr & Mrs Ahuja not together = Total Cases where Mr & Mrs Sharma together - Arrangements where Mr & Mrs Sharma sit together & Mr & Mrs Ahuja sit together
For Mr & Mrs Sharma sitting together consider them one unit and arrange them within themselves later
Seating Arrangement in a circle = (n - 1)!
So there are 7 people => 6 people & 7th one Mr & Mrs Sharma
Total cases where Mr & Mrs Sharma
Together = 6! × 2!
Arrangements where Mr & Mrs Sharma
Together & Mr. & Mrs Ahuja Together = 5! x 2! x 2!
Cases where Mr & Mrs Sharma
Together & Mr & Mrs Ahuja no together = 6! x 2! (5! x 2! x 2!)
= 5! × 2! (6 – 2)
= 240 x 4
= 960
Alternate Method ?
Arrange Mr & Mrs Sharma along with 4 persons excluding Mr & Mrs Ahuja from the group.
= 4! X 2!
(Formula ? Arrangement in circular table = (∩ - 1)!
The spaces created b/w arrangements is 4 + 1 = 5
Select any 2 places & arrange Mr & Mrs Ahuja so they will never be together
= 4! X 2! X 5P2 = 960