Question

A. How many ways are there to make 35 cents change in 1952 pennies, 1959 pennies and 1964 nickels? B. In 1952 pennies, 1959 pennies, 1964 nickels and 1971 quarters?

Answer 1

Answer:

Given that:

A) How many ways are there to make 35 cents change in 1952 pennies, 1959 pennies and 1964 nickels?

Say that we have no nickels. Then all 35 cents must be pennies. The distribution for this can be: 0,35; 1,34;...; 35,0, for a total of 36 possibilities. If there is one nickel, then 30 of the cents must be pennies, and again we have: 0,30; 1,29;...; 30,0, for a total of 31 possibilities. Continuing along this trend, there will be 26 possibilities with 25 cents in pennies, 21 possibilities with 20 cents, all the way to six possibilities with 5 cents. Of course, we could also have 7 nickels and no pennies. In total, there are

36+31+26+21+16+11+6+1=148 options.

B)  In 1952 pennies, 1959 pennies, 1964 nickels and 1971 quarters?

If we ignore the quarters, then there are 148 options, from the previous question. In addition, if we have 1 quarter, then we can have:
10 pennies, which has 11 possibilities. We can also have 1 nickel and 5 pennies, which provides 6 possibilities, or 2 nickels and no pennies, which affords 1 additional possibility. In all, there are

148+11+6+1=166 options.

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