Assuming-you-have-enough-coins-of-1-5-10-25-and-50cents-In-how-many-ways-can-you-make-a-change-for-1dollar-

Question Number 117192 by Lordose last updated on 10/Oct/20

Assuming you have enough coins

of 1, 5, 10, 25, and 50 cents . In how

many ways can you make a change for 1 dollar .

Answered by mr W last updated on 10/Oct/20

a + 5 b + 10 c + 25 d + 50 e = 100

(1 + x + x^{2} + x^{3} + \dots) \times

(1 + x^{5} + x^{10} + x^{15} + \dots) \times

(1 + x^{10} + x^{20} + x^{30} + \dots) \times

(1 + x^{25} + x^{50} + x^{75} + \dots) \times

(1 + x^{50} + x^{100} + x^{150} + \dots)

= \frac{1}{(1 - x) (1 - x^{5}) (1 - x^{10}) (1 - x^{25}) (1 - x^{50})}

c o e f f i c i e n t o f t e r m x^{100} i s 292, i . e .

w e h a v e 292 w a y s t o c h a n g e 1 d o l l a r .

Commented by Lordose last updated on 10/Oct/20

Thanks sir

Commented by Lordose last updated on 10/Oct/20

can you explain sir ?

Commented by Lordose last updated on 10/Oct/20

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Commented by mr W last updated on 10/Oct/20

i u s e d g e n e r a t i n g f u n c t i o n m e t h o d

t o f i n d t h e n u m b e r o f n o n - n e g a t i v e

i n t e g e r s o l u t i o n s o f e q u a t i o n

a + 5 b + 10 c + 25 d + 50 e = 100

Commented by Lordose last updated on 10/Oct/20

Thanks sir ��