3 persons (1 couple and 1 single) are seated at random in a raw of 5 chairs. What is the probability that the couple DOES NOT sit together?
5/7
4/5
2/5
3/5
11/18
any help is welcome!
Probability 3 persons seated
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IMO
Total Number of ways the 3 people can be seated on 5 chairs is 5C3 = 10
The number of ways they can be seated with the couple sitting together is 4C2
The probability that the couple will SIT TOGETHER is 4C2/5C3 = 6/10
so the probability that the couple DOES NOT SIT TOGETHER should be
1-6/10 = 4/10 => 2/5
Please correct me if am wrong.
Total Number of ways the 3 people can be seated on 5 chairs is 5C3 = 10
The number of ways they can be seated with the couple sitting together is 4C2
The probability that the couple will SIT TOGETHER is 4C2/5C3 = 6/10
so the probability that the couple DOES NOT SIT TOGETHER should be
1-6/10 = 4/10 => 2/5
Please correct me if am wrong.
Nethra
I think you have to take order into account, since, for instance, if the three people sit on chairs 1, 4 and 5, you'll have different cases depending on where the loner sits.
Number of ways in which the 3 people can be seated:
5*4*3 = 60
Number of ways in which the couple will be seated together:
4*3*2 = 24
If A and B are the members of the couple and S the other chairs:
A B S S S
S A B S S
S S A B S
S S S A B
B A S S S
etc...
We have 8 of those, and for every one of them the loner can be seated on 1 of the three different chairs left, and therefore we need to multiply by 3...
The probability that the couple sits together is then 24/60 = 2/5
and the probability that the couple DOES NOT sit together: 3/5
Number of ways in which the 3 people can be seated:
5*4*3 = 60
Number of ways in which the couple will be seated together:
4*3*2 = 24
If A and B are the members of the couple and S the other chairs:
A B S S S
S A B S S
S S A B S
S S S A B
B A S S S
etc...
We have 8 of those, and for every one of them the loner can be seated on 1 of the three different chairs left, and therefore we need to multiply by 3...
The probability that the couple sits together is then 24/60 = 2/5
and the probability that the couple DOES NOT sit together: 3/5