Q. 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?

Explanation :

Different sums that can be formed with different denominations

There are five denominations in total and we need to choose at least three of them to form a sum. We can use the formula for combinations to calculate the number of ways to choose k items from n items:

Formula: C(n,k) = n! / (k!(n-k)!)
where n is the total number of items and k is the number of items being chosen.

Calculations:
1. Choosing three denominations from five:
C(5,3) = 5! / (3!(5-3)!) = 10

2. Choosing four denominations from five:
C(5,4) = 5! / (4!(5-4)!) = 5

3. Choosing all five denominations:
Only one way possible = 1

Total number of different sums = 10 + 5 + 1 = 16