Problem 3. Solve the following counting problems (show your justifications): (a) How many permutations of the ten letters A, B, C, D, E, F, G, H, I, J (b) How many permutations of the ten letters A, B, C, D, E, F, G, H, I, J (c) How many permutations of the ten letters A, B, C, D, E, F, G, H, I, J (d) How many permutations of the ten letters A, B, C, D, E, F, G, H, I, J (e) How many permutations of the ten letters A, B, C, D, E, F, G, H, I, J begin with "B"? have "B" in one of the first three locations? have three vowels before the seven consonants? neither begin nor end with "BAD"? do not have the vowels next to each other