The letters {a, b, c, d, e, f, g} are put in a random order. Each permutation is equally likely. Define the following events:

A: The letter b falls in the middle (with three before it and three after it)

B: The letter c appears to the right of b, although c is not necessarily immediately to the right of b. For example, "agbdcef" would be an outcome in this event.

C: The letters "def" occur together in that order (e.g. "gdefbca")

a. Calculate P(A), P(B), P(C).

b. Calculate P(A|C)

c. Calculate P(B|C)

d. Calculate P(A|B)