If someone could give answers and explain, it would be greatly appreciated. Help required studying for a final.
One hundred tickets, numbered 1,2,3,…,100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti).
A) How many ways are there to award the prizes?
B) How many ways are there to award the prizes if the person holding ticket 47 wins the grand prize?
C) How many ways are there to award the prizes if the person holding ticket 47 wins one of the prizes?
D) How many ways are there to award the prizes if the person holding ticket 47 does not win a prize?
E) How many ways are there to award the prizes if the people holding tickets 19 and 47 both win prizes?
F) How many ways are there to award the prizes if the people holding tickets 19, 47, 73, and 97 all win prizes?
G) How many ways are there to award the prizes if none of the people holding tickets 19, 47, 73, and 97 wins a prize?
H) How many ways are there to award the prizes if the grand prize winner is a person holding ticket 18, 47, 73, or 97?
I) How many ways are there to award the prizes if the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes?