How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank con- tain if it has 20 coins in it?

10626 different combinations. This is a "Stars and Bars" type of problem with their being 20 "stars" and 5 bins which results in (5-1 = 4) "bars". The problem can be rephrased as "How many distinct values of x1,x2,x3,x4,x5 can you make for the following equation?" x1 + x2 + x3 + x4 + x5 = 20 The general equation to this problem is C=(n+k-1)!/(n!(k-1)!) where C = number of combinations n = number of stars k = number of bins So substitute the known value and solve. C=(20+5-1)!/(20!(5-1)!) C=24!/(20!4!) C= 24*23*22*21*20!/(20!4!) C= 24*23*22*21/(4*3*2*1) C= 24*23*22*21/24 C= 23*22*21/1 C= 23*22*21 C= 10626

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