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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?
- a)10
- b)15
- c)14
- d)16
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
How many different sums can be formed with the denominations Rs. 50, R...
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
option D is correct
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
Most Upvoted Answer
How many different sums can be formed with the denominations Rs. 50, R...
Solution:
To find the number of different sums that can be formed with at least three denominations, we need to use combination.
Step 1: Find the number of combinations of denominations that can be taken three at a time
We can take three denominations out of five in 5C3 ways, which is equal to 10.
Step 2: Find the number of combinations of denominations that can be taken four at a time
We can take four denominations out of five in 5C4 ways, which is equal to 5.
Step 3: Find the number of combinations of denominations that can be taken five at a time
We can take all five denominations in 1 way.
Step 4: Find the total number of different sums that can be formed
To find the total number of different sums, we need to add the number of sums that can be formed with three denominations, four denominations, and five denominations.
Total number of different sums = 10 + 5 + 1 = 16
Hence, the correct answer is option D, 16.
To find the number of different sums that can be formed with at least three denominations, we need to use combination.
Step 1: Find the number of combinations of denominations that can be taken three at a time
We can take three denominations out of five in 5C3 ways, which is equal to 10.
Step 2: Find the number of combinations of denominations that can be taken four at a time
We can take four denominations out of five in 5C4 ways, which is equal to 5.
Step 3: Find the number of combinations of denominations that can be taken five at a time
We can take all five denominations in 1 way.
Step 4: Find the total number of different sums that can be formed
To find the total number of different sums, we need to add the number of sums that can be formed with three denominations, four denominations, and five denominations.
Total number of different sums = 10 + 5 + 1 = 16
Hence, the correct answer is option D, 16.
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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?a)10b)15c)14d)16Correct answer is option 'D'. Can you explain this answer?
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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?a)10b)15c)14d)16Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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?a)10b)15c)14d)16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?a)10b)15c)14d)16Correct answer is option 'D'. Can you explain this answer?.
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