Question

How many different sums can be formed with the denominations 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 1

Correct Answer - Option 1 : 16

Given:

Denominations 50, 100, 200, 500 and 2,000

Calculation:

Let each denomination is single

Total denominations = 5

According to the question:

Taking at least three denominations at a time

⇒ 3 denominations, 4 denominations, 5 denominations

⇒ 3 denominations out of 5 in ⁵C₃ = 10 ways

⇒ 4 denominations out of 5 in 5C₄ = 5 ways

⇒ 5 denominations out of 5 in 5C₅ = 1 way

Total ways = 10 + 5 + 1 = 16

∴ The answer is 16.