MHB A question about the law of total probability

[lola19991]

Dan put n different kinds of cheese in a row randomly, so that between two kinds of cheese there is a space. Then he puts a pickle on one of the n-1 spaces between the cheeses randomly. What is the probability of goat cheese and parmesan cheese (2 from n kinds of cheese) to be in the different sides of the pickle?

I know that I need to use law of total probability and define A_i as the pickle is found in the space number I from n-1 spaces, but I am stuck.

 

[tkhunny]

Dan put n different kinds of cheese in a row randomly, so that between two kinds of cheese there is a space. Then he puts a pickle on one of the n-1 spaces between the cheeses randomly. What is the probability of goat cheese and parmesan cheese (2 from n kinds of cheese) to be in the different sides of the pickle?

I know that I need to use law of total probability and define A_i as the pickle is found in the space number I from n-1 spaces, but I am stuck.

Don't we first need the probability that GOAT and PARM end up together? Perhaps what may seem like an odd approach, tape those two together and see if it is easier to count the possibilities.