Cash permutations
Using only notes of denominations $5, $10, $20,
How many ways can you give me $100 using at most 6 $10 notes?
The answer is 30.
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1 solution
Moderator note:
Hm, can you explain how "use series expansion to further simplify it"? It seems to me the second line doesn't really help to simplify the scenario.
Coefficient of x 1 0 0 in ( 1 + x 5 + x 1 0 + x 1 5 + . . . ) ( 1 + x 1 0 + x 2 0 + x 3 0 + . . . x 6 0 ) ( 1 + x 2 0 + x 4 0 + x 6 0 + . . . )
Coefficient of x^100 in (1+x^5)^(-1) (1+x^20)^(-1) (1+x^10 +x^20 +x^30 + ...x^60)\
Use Series expansion to further simplify it