couples together

[debarshi]

Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

Is the answer 2/5 or 3/5 ? Official Answer is 2/5 but i think it should be 3/5. Can you help?

[12rk34]

Pls. check this:
http://www.urch.com/forums/gmat-prob...lp-needed.html (Probability quest..Help needed)

[seahawk]

24 ways both couples are together...
48 ways only one couple is together...
120 ways of arrangement ...
48 ways none of the couple is together

answer = 2/5

[rajatmeh]

Both couples sit together=2*2*!3=24
Assume A is couple 1 (together), B1 and B2 are couple 2 and C is single person

AB1CB2
AB2CB1
B1AB2C
B1ACB2
B2AB1C
B2ACB1
B1CAB2
CB1AB2
B2CAB1
CB2AB1
B2CB1A
B1CB2A

Only 1st couple sits together=2*12=24 (multiplying by 2 as couple A can also be arranged in 2 ways)
Only 2nd couple sits together=2*12=24 (same as above)

Total = 24+24+24=72

Total ways in which 5 persons can be seated = !5=120

Prob = 1-72/120=48/120=2/5