How many different sums can be formed with the denominations ₹ 50, ₹ 100, ₹ 200, ₹ 500 and ₹ 2,000 taking at…
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?
16
15
14
10
Solution
Number of ways to choose at least 3 out of 5 denominations $= \binom{5}{3} + \binom{5}{4} + \binom{5}{5} = 10 + 5 + 1 = 16$. Since all denominations are distinct values, every selection gives a distinct sum. Hence 16 different sums.