Question

$3$ Indian and $3$ American men and their wives are to be seated round a circular table. Let $m$ denotes the number of ways when the Indian couples are together and $n$ denotes the number of ways when all the six couples are together. If $m=kn$ then $k$ equal

• A. $36$
• B. $42$
• C. $45$
• D. $48$

Answer 1

The correct option is B $42$

There are total 12 peoples and 6 pairs

when the Indian couples are together

Therefore 3pairs and 6 people and pairs can interchange

let clockwise and anti clock wise be different

$(9-1)!\times 2\times 2\times 2=8.8!$

now all peoples sit in pairs

$(6-1)!\times 2^6=2^6.5!=n$

comparing

$8.8!=2^6.7.6.5!=42n$

Therefore k=42