Determine the followingprobabilities (remember to fully justify your responses):

1. Problem #1: the arrangement does not contain the letters F and B next to each other?
2. Problem #2: none of the people holding tickets 5, 19, 23, and 29 wins a prize?
3. Problem #3: there are more heads than tails in those ten flips?
4. Problem #4: your piece Y ends up in the position (b)?

here is Problem #1

How many permutations of all the letters {A,B,C,D,E,F,G}

1. Contain the string BCD?
2. Contain the strings BA and GF?
3. Contain letter A or letter C in the middle?
4. Contain the letters F and B next to each other