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

Correct Answer: (A) 16

There are 5 distinct currency denominations: ₹ 50, ₹ 100, ₹ 200, ₹ 500, and ₹ 2,000. Any subset sum formed by these values is unique. Taking at least three denominations at a time means choosing 3, 4, or 5 denominations: $\left(\genfrac{}{}{0px}{}{5}{3}\right)+\left(\genfrac{}{}{0px}{}{5}{4}\right)+\left(\genfrac{}{}{0px}{}{5}{5}\right)=10+5+1=16$$\binom{5}{3}$ + $\binom{5}{4}$ + $\binom{5}{5}$ = 10 + 5 + 1 = 16 distinct sums.