probability

I think that would be 2 out of 6 because there are two keys and six possibilities in which one of the keys might go.

nice graphics Thanks for the explanation. I hope I don't run into lots of probability

I get 1/3 too.

Consider the two keys as "one". Now, since we have 5 spaces in the chain, the "one" key can be arranged in the chain in 5 ways. Now, each "one" key can be in the orientation, AB or BA. Hence, for each 5 slots above, AB and BA are possible. Hence, 10 ways to have the two keys together.

Now, consider the total no. of ways to put the 2 keys. When we put key A, we have 5 slots. Hence 5. Now, the chain has 6 keys. If we put an additional key, B, into the chain, we have 6 ways to do so. Hence, total nos. is 5x6 = 30 ways.

Hence, probability = 10/30 = 1/3.

Am I right?

Accroding to me following could be the answer.

1. There are in total 7 keys and two newly added keys need to be together.
2. In this case consider two keys as one. So now in total we have 6 keys, 5 old keys and 2 newly added keys which are considered as one because they need to be together.

Using this answer would be 1/6.

let me know if I am wrong.