Question

There are six chairs in a row. Person A picks one of the chairs at random. Then Person B picks a chair at random from the five chairs that remain. Find the chance that they pick chairs that are next to each other.

Answer 1

Let's label the 6 chairs as 6 slots

The chair on the very left is slot 1. The chair furthest on the right is slot 6.

-----------------------------------------------------------------

Case 1) A chooses slot 1

P(A chooses slot 1) = 1/6

P(B chooses slot 2) = 1/5

Multiply them out to get (1/6)*(1/5) = 1/30

-----------------------------------------------------------------

Case 2) A chooses slot 6

P(A chooses slot 6) = 1/6

P(B chooses slot 5) = 1/5

Multiply them out to get (1/6)*(1/5) = 1/30

-----------------------------------------------------------------

Case 3) A chooses slots 2, 3, 4, or 5

P(A chooses slots 2, 3, 4, or 5) = 4/6 = 2/3

P(B chooses a slot next to A) = 2/5 ... Note: there are 2 chairs on either side of slot 2, 3, 4, or 5

Multiply them out to get (2/3)*(2/5) = 4/15

Answer 2

120?

Answer 3

wait nvm

Answer 4

chance...

Answer 5

Now add up the probabilities found in cases 1 through 3

1/30 + 1/30 + 4/15

1/30 + 1/30 + 8/30

10/30

1/3

Answer 6

Yes that is correct