Probability

[Jeyanthi R]

There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel. How many ways it can be done ?
Solution: Because of symmetry, the number of ways that Bob is left to Rachel is exactly 1/2 of all possible ways:

 

[Deleted member 4993]

There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel. How many ways it can be done ?
Solution: Because of symmetry, the number of ways that Bob is left to Rachel is exactly 1/2 of all possible ways:

What do you want to know?

 

[pka]

There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel. How many ways it can be done ?
Solution: Because of symmetry, the number of ways that Bob is left to Rachel is exactly 1/2 of all possible ways:

I would argue the answer is \(\dfrac{5!}{2}=60.\) because the question does not say they sit together just Bob is always left to Rachel.

 

[Dr.Peterson]

There are 5 chairs. Bob and Rachel want to sit such that Bob is always left to Rachel. How many ways it can be done ?
Solution: Because of symmetry, the number of ways that Bob is left to Rachel is exactly 1/2 of all possible ways:

As I read it, only the two people are present, so Bob and Rachel choose two chairs and the other three are left empty. You are right; but it could also be described as merely choosing two of the five chairs, and Bob always takes the one on the left: [MATH]_5C_2 = \frac{5!}{2!3!} = 10[/MATH].

If there are 5 people, and we distinguish where each one sits, not just Bob and Rachel, then pka is right.

 

[Steven G]

I can only assume that the chairs are in a line. If they were in a circle then things change drastically.

You can count the situation easily so there is not doubt of the answer.

Number the seats 1 to 5 from left to right.

If Rachel sits in 1st chair, then Bob can choose from 0 chairs to sit in.
If Rachel sits in 2nd chair, then Bob can choose from 1 chairs to sit in.
If Rachel sits in 3rd chair, then Bob can choose from 2 chairs to sit in.
If Rachel sits in 4th chair, then Bob can choose from 3 chairs to sit in.
If Rachel sits in 5th chair, then Bob can choose from 4 chairs to sit in.

The total number for Bob is 10.

 

[Jeyanthi R]

Is there another possible answer? If so,explain

 

[Steven G]

Is there another possible answer? If so,explain

There are two answers, yes, and they have been both given.

One answer assumes that only Bob and Rachel will sit (10) and the other solution assumes that 5 people will sit but Bob will be to the left of Rachel (60)