(1) In how many ways can the selection be made?

Question

Assume that you have 7 dimes and 4 quarters (all distinct), and you select 5 coins.

 

(1) In how many ways can the selection be made?

(2) In how many ways can the selection be made if all the coins are dimes?

(3) In how many ways can the selection be made if you select 2 dimes and 3 quarters?

(4) In how many ways can the selection be made so that at least 4 coins are dimes?

 

 

Answer 1

(1) Total number of coins = 11. So total number of combinations is 11 choose 5 = 462

(2) Total number of dimes = 7. So total number of combinations is 7 choose 5 = 21

(3) (7 choose 2)(4 choose 3) = 84

(4) At least 4 coins are dimes means 1) 4 coins are dimes and 1 is quarter 2) 5 coins are dimes. Add the two cases

(7 choose 4)(4 choose 1) + (7 choose 5) = 161