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In how many ways can a person give Rs 500 using Rs 100 and Rs 20 notes, given 16 notes of Rs 20 are available?
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Solution: Step 1: Let the number of Rs 100 notes be y and Rs 20 notes be z
Step 2: 100y + 20z = 500
Step 3: Given z <= 16, and both y, z are integers
Step 4: Maximum amount using Rs 20 notes = 16 * 20 = 320
Step 5: Possible combinations: (y, z) = (5, 0), (3, 10), (1, 20) but z cannot exceed 16 and must be even for easy calculation
Step 6: Checking valid combinations: (y, z) = (5, 0), (3, 10)
Step 7: Only 3 valid combinations exist