Question

1.) There are 16 juniors and 8 seniors in the Chess Club. If the club

members decide to send 9 juniors to a tournament, how many different
possibilities are there?
2.) How many different ways can 3 cards be drawn from a deck of 52
cards without replacement?
3.) How many different ways can 3 cards be drawn from a deck of 52
cards with replacement?
4.) A corporation has 5 officers to choose from which 3 are selected
to comprise the board of directors. How many combinations are there?
5.) A combination lock has the numbers 1 to 40 on each of three
consecutive tumblers. What is the probability of opening the lock in
ten tries?

Answer 1

1.) There are 16 juniors and 8 seniors in the Chess Club. If the club members decide to send 9 juniors to a tournament, how many different possibilities are there?

(16 over 9) = 16!/(9!*7!) = 11440

2.) How many different ways can 3 cards be drawn from a deck of 52 cards without replacement?

52*51*50 = 132600

3.) How many different ways can 3 cards be drawn from a deck of 52 cards with replacement?

52^3 = 140608

4.) A corporation has 5 officers to choose from which 3 are selected to comprise the board of directors. How many combinations are there?

(5 over 3) = 5!/(3! * 2!) = 10

5.) A combination lock has the numbers 1 to 40 on each of three consecutive tumblers. What is the probability of opening the lock in ten tries?

10/40^3 = 1/6400