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Question 33

The number of ways in which coins of denominations of rupees 2, 5 and, 10 can be combined to make a value of rupees 50 is

Solution

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$$2a + 5b + 10c = 50$$ with $$a, b, c \geq 0$$ integers.

For each $$c$$: $$2a + 5b = 50 - 10c$$. Number of $$(a,b)$$ with $$b$$ even satisfying:

  • $$c=0$$: $$b \in \{0,2,4,6,8,10\}$$ → 6
  • $$c=1$$: 5; $$c=2$$: 4; $$c=3$$: 3; $$c=4$$: 2; $$c=5$$: 1

Total $$= 6+5+4+3+2+1 = \mathbf{21}$$.

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