OA is D

My Answer is 2/5

Let the couple be Aa Bb and C( single person )

out of 5 places

Assume if C takes the 1st place

A can take the first place in 4 ways , a cannot take the second place. it has to be taken by wither B or b hence is 2 ways and the last 2 places in 1 way

hence 1*4*2*1*1 = 8 ways

Assume C takes the 5 th place - 8 ways same as above.

Assume C takes the 2 second place its (4*1*2*1*1) = 8 ways

Assume C takes the 4th place - 8 ways same as above

If C takes the 3rd place

1st place in 4 ways , 2nd place in 2 ways , 4th place in 2 place and 5th place in 1 way

hence its 4*2*1*2*1 = 16.

therefore its

8+8+8+8+16 = 48 ways.

5 people can arrange themselves in 5! = 120

thus the probability is 48/120 which is 2/5.

hope it helps..

i cant give u a better explanation than Ian


@sudhir

we all need a quicker method


https://www.beatthegmat.com/war-of-the-r ... 12457.html

heres another approach

total ways is 5!

one couple sits together, hence the number of ways is 2! x 4!

the no. of ways other couple can sit is 2! x 4!



total = 2 x 2! x 4! ways

But in above cases include both couples are together twice.
hence we need to subtract one.

The number of ways both couples sit together is 3! x 2! x 2!.

Probability that any of the couples sitting in adjacent chairs =

= [(2 x 2! x 4! ) - (3! x 2! x 2!)]/5! =3/5

neither of the couples sit together in adjacent chairs = 1 - 3/5 = 2/5

Hope its better raunekk and faster as well...

sudhir3127 wrote:My Answer is 2/5

Let the couple be Aa Bb and C( single person )

out of 5 places

Assume if C takes the 1st place

A can take the first place in 4 ways , a cannot take the second place. it has to be taken by wither B or b hence is 2 ways and the last 2 places in 1 way

hence 1*4*2*1*1 = 8 ways

Assume C takes the 5 th place - 8 ways same as above.

Assume C takes the 2 second place its (4*1*2*1*1) = 8 ways

Assume C takes the 4th place - 8 ways same as above

If C takes the 3rd place

1st place in 4 ways , 2nd place in 2 ways , 4th place in 2 place and 5th place in 1 way

hence its 4*2*1*2*1 = 16.

therefore its

8+8+8+8+16 = 48 ways.

5 people can arrange themselves in 5! = 120

thus the probability is 48/120 which is 2/5.

hope it helps..

A can take the first place in 4 ways , a cannot take the second place. it has to be taken by wither B or b hence is 2 ways and the last 2 places in 1 way

hence 1*4*2*1*1 = 8 ways
Can you explain how you get 1*4*2*1*1= 8 ways? I have the A takes the first place, but come up with more than 4 ways. Please help me out.

Let me try:

Couples A1A2 B1B2 and single S

lets have the A1B2 A2B1 and S as three units

3x2x1=6 ways both couples can interchange so 2x2 = 4

4x6 =24

since we can also have A1B1 and A2B2 it is 24 too

48/5!

Assume C takes the 2 second place its (4*1*2*1*1) = 8 ways

Sudhir,
Why is this not

4*1*3*1*1 = 12??

I got it sorry!

If its a,B,b left it has to be B or b for the 3rd spot since a has to come between them!!!