How many ways could you be able to make 141 dollars using only 20's 5's and 1's each used atleast once?

Answer 1

To answer your question, there are 84 possible ways. Once you find out how many different ways there are for 6 twenties and 5 twenties, you should notice the pattern that shows that the total amount for each twenty goes up by four each time, due to ever twenty equaling 4 fives, giving four more possibilities. Since there are only 6 twenties you can use, simply add 4+8+12+16+20+24 which equals 84. Below, I have written each possibility for your use.

(6*20)+(4*5)+(1*1)

(6*20)+(3*5)+(6*1)

(6*20)+(2*5)+(11*1)

(6*20)+(1*5)+(16*1)

(5*20)+(8*5)+(1*1)

(5*20)+(7*5)+(6*1)

(5*20)+(6*5)+(11*1)

(5*20)+(5*5)+(16*1)

(5*20)+(4*5)+(21*1)

(5*20)+(3*5)+(26*1)

(5*20)+(2*5)+(31*1)

(5*20)+(1*5)+(36*1)

(4*20)+(12*5)+(1*1)

(4*20)+(11*5)+(6+1)

(4*20)+(10*5)+(11*1)

(4*20)+(9*5)+(16*1)

(4*20)+(8*5)+(21*1)

(4*20)+(7*5)+(26*1)

(4*20)+(6*5)+(31*1)

(4*20)+(5*5)+(36*1)

(4*20)+(4*5)+(41*1)

(4*20)+(3*5)+(46*1)

(4*20)+(2*5)+(51*1)

(4*20)+(1*5)+(56*1)

(3*20)+(16*5)+(1*1)

(3*20)+(15*5)+(6*1)

(3*20)+(14*5)+(11*1)

(3*20)+(13*5)+(16*1)

(3*20)+(12*5)+(21+1)

(3*20)+(11*5)+(26*1)

(3*20)+(10*5)+(31*1)

(3*20)+(9*5)+(36*1)

(3*20)+(8*5)+(41*1)

(3*20)+(7*5)+(46*1)

(3*20)+(6*5)+(51*1)

(3*20)+(5*5)+(56*1)

(3*20)+(4*5)+(61*1)

(3*20)+(3*5)+(66*1)

(3*20)+(2*5)+(71*1)

(3*20)+(1*5)+(76*1)

(2*20)+(20*5)+(1*1)

(2*20)+(19*5)+(6*1)

(2*20)+(18*5)+(11*1)

(2*20)+(17*5)+(16*1)

(2*20)+(16*5)+(21*1)

(2*20)+(15*5)+(26*1)

(2*20)+(14*5)+(31*1)

(2*20)+(13*5)+(36*1)

(2*20)+(12*5)+(41*1)

(2*20)+(11*5)+(46*1)

(2*20)+(10*5)+(51*1)

(2*20)+(9*5)+(56*1)

(2*20)+(8*5)+(61*1)

(2*20)+(7*5)+(66*1)

(2*20)+(6*5)+(71*1)

(2*20)+(5*5)+(76*1)

(2*20)+(4*5)+(81*1)

(2*20)+(3*5)+(86*1)

(2*20)+(2*5)+(91*1)

(2*20)+(1*5)+(96*1)

(1*20)+(24*5)+(1*1)

(1*20)+(23*5)+(6*1)

(1*20)+(22*5)+(11*1)

(1*20)+(21*5)+(16*1)

(1*20)+(20*5)+(21*1)

(1*20)+(19*5)+(26*1)

(1*20)+(18*5)+(31*1)

(1*20)+(17*5)+(36*1)

(1*20)+(16*5)+(41*1)

(1*20)+(15*5)+(46*1)

(1*20)+(14*5)+(51*1)

(1*20)+(13*5)+(56*1)

(1*20)+(12*5)+(61*1)

(1*20)+(11*5)+(66*1)

(1*20)+(10*5)+(71*1)

(1*20)+(9*5)+(76*1)

(1*20)+(8*5)+(81*1)

(1*20)+(7*5)+(86*1)

(1*20)+(6*5)+(91*1)

(1*20)+(5*5)+(96*1)

(1*20)+(4*5)+(101*1)

(1*20)+(3*5)+(106*1)

(1*20)+(2*5)+(111*1)

(1*20)+(1*5)+(116*1)