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Old 2013-04-03, 21:50   #22
Raman
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"Mr. Tuch"
Dec 2007
Chennai, India

23518 Posts
Default Three coins denominations

Three coins denominations
Coins Into The Box
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We have 5 types of coins

Half Dollar (H) = 50 ¢
Quarter (Q) = 25 ¢
Dime (D) = 10 ¢
Nickel (N) = 5 ¢
Penny (P) = 1 ¢

Given that you have to pick up 3 coins from these, not necessarily distinct, how many distinct values of the total cash is possible? Possible values are

P + P + P = 3 ¢
N + P + P = 7 ¢
N + N + P = 11 ¢
D + P + P = 12 ¢
N + N + N = 15 ¢
D + N + P = 16 ¢
D + N + N = 20 ¢
D + D + P = 21 ¢
D + D + N = 25 ¢
Q + P + P = 27 ¢
D + D + D = 30 ¢
Q + N + P = 31 ¢
Q + N + N = 35 ¢
Q + D + P = 36 ¢
Q + D + N = 40 ¢
Q + D + D = 45 ¢
Q + Q + P = 51 ¢
H + P + P = 52 ¢
Q + Q + N = 55 ¢
H + N + P = 56 ¢
H + N + N = 60 ¢
Q + Q + D = 60 ¢
H + D + P = 61 ¢
H + D + N = 65 ¢
H + D + D = 70 ¢
Q + Q + Q = 75 ¢
H + Q + P = 76 ¢
H + Q + N = 80 ¢
H + Q + D = 85 ¢
H + Q + Q = 100 ¢
H + H + P = 101 ¢
H + H + N = 105 ¢
H + H + D = 110 ¢
H + H + Q = 125 ¢
H + H + H = 150 ¢
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