How many different sums can be formed with the denomination

How many different sums can be formed with the denomination Rs. 50, Rs. 100, Rs. 200, Rs. 500, and Rs. 2,000 taking at least three denominations at a time?

  1. 16
  2. 15
  3. 14
  4. 10
  • Answer: The correct option is A
  • Explanation:

    Number of denominations = 5

    Case I: Using all the 5 denominations

    Number of ways = 1

    Case II: Using 4 denominations

    Using 4 denominations means we need to leave out 1 of the denomination.

    Number of ways to leave out one of the denomination = 5C1 = 5

    Case III: Using 3 denominations

    Number of ways to use three denominations = 5C3 = 5C2 = (5 × 4)/2 = 10

    Hence, the number of different sums that can be formed = 1 + 5 + 10 = 16
  • Exam Year: 2020