5. How many different sums can be formed
with the denominations P 50, 100,
P200, P500 and 2,000 taking at
least three denominations at a time?
Answers
Given : denominations P 50, 100, P200, P500 and 2,000
To Find : How many different sums can be formed taking at
least three denominations at a time
Solution:
Assuming Each denomination is single
Total denominations 5
taking at least three denominations at a time
=> 3 Denominations , 4 Denomination , 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
All possible cases : Total
50 100 200 250
50 100 500 650
50 100 2000 2150
50 200 500 750
50 200 2000 2250
50 500 2000 2550
100 200 500 800
100 200 2000 2300
100 500 2000 2600
200 500 2000 2700
Total
50 100 200 500 850
50 100 200 2000 2350
50 100 500 2000 2650
50 200 500 2000 2750
100 200 500 2000 2800
50 100 200 500 2000 2850
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