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Consider S = (1, 2, 3,... 10). In how many ways two numbers from S can be selected so that the sum of the numbers selected is a double digit number?
- a)36
- b)16
- c)29
- d)9C2 - 5C2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider S = (1, 2, 3,... 10). In how many ways two numbers from S can...
Given, S=(1, 2, 3, …,10).
Two numbers from S are to be selected, such that the sum of the numbers selected is a double-digit number.
If one of the selected number is 10, then, the other number can be any one of 1, 2, 3, ..., 9. So, the number of ways =9.
If one of the selected number is 9, then, the other number can be any one of 1, 2, 3, ..., 8. So, the number of ways =8.
If one of the selected number is 8, then, the other number can be any one of 2, 3, ..., 7. So, the number of ways =6.
If one of the selected number is 7, then, the other number can be any one of 3, 4, ..., 6. So, the number of ways =4.
If one of the selected number is 6, then, the other number can be any one of 4, 5. So, the number of ways =2.
⇒ Total number of ways =9+8+6+4+2=29
Hence, the correct answer is 29.
Most Upvoted Answer
Consider S = (1, 2, 3,... 10). In how many ways two numbers from S can...
Points to remember for this question:
You do not take the same number twice i.e (10,10) (6,6) (7,7)(5,5) are not taken into consideration.
We are selecting two numbers but the order does not matter, so (10,1) and (1,10) give us one count, they are essentially the same.
Now we can make all the possible sets:
let's start backwards:
10 + {1,2,3,4,5,6,7,8,9} = 9 ways.
9 +{1,2,3,4,5,6,7,8} = 8 ways.
8 + {2,3,4,5,6,7} = 6 ways.
7 + {3,4,5,6} = 4 ways.
6 + {4,5} = 2 ways
hence 9+8+6+4+2 = 29 ways.
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Community Answer
Consider S = (1, 2, 3,... 10). In how many ways two numbers from S can...
Approach:
To find the number of ways two numbers from S can be selected so that the sum of the numbers selected is a double-digit number, we can follow the below approach:
- Find the total number of ways of selecting two numbers from S.
- Find the number of ways of selecting two numbers from S such that the sum is a single digit number.
- Subtract the number of ways found in step 2 from the total number of ways found in step 1 to get the required number of ways.
Calculation:
Total number of ways of selecting two numbers from S = 10C2 = 45.
Number of ways of selecting two numbers from S such that the sum is a single digit number:
- (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9)
- (2,1), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8)
- (3,1), (3,2), (3,4), (3,5), (3,6)
- (4,1), (4,2), (4,3), (4,5)
- (5,1), (5,2), (5,3), (5,4)
- (6,1), (6,2), (6,3)
- (7,1), (7,2)
- (8,1)
- Total number of ways = 29.
Required number of ways = Total number of ways - Number of ways of selecting two numbers from S such that the sum is a single digit number
= 45 - 29
= 16.
Therefore, the required number of ways two numbers from S can be selected so that the sum of the numbers selected is a double-digit number is 16. Hence, option (c) is the correct answer.
To find the number of ways two numbers from S can be selected so that the sum of the numbers selected is a double-digit number, we can follow the below approach:
- Find the total number of ways of selecting two numbers from S.
- Find the number of ways of selecting two numbers from S such that the sum is a single digit number.
- Subtract the number of ways found in step 2 from the total number of ways found in step 1 to get the required number of ways.
Calculation:
Total number of ways of selecting two numbers from S = 10C2 = 45.
Number of ways of selecting two numbers from S such that the sum is a single digit number:
- (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9)
- (2,1), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8)
- (3,1), (3,2), (3,4), (3,5), (3,6)
- (4,1), (4,2), (4,3), (4,5)
- (5,1), (5,2), (5,3), (5,4)
- (6,1), (6,2), (6,3)
- (7,1), (7,2)
- (8,1)
- Total number of ways = 29.
Required number of ways = Total number of ways - Number of ways of selecting two numbers from S such that the sum is a single digit number
= 45 - 29
= 16.
Therefore, the required number of ways two numbers from S can be selected so that the sum of the numbers selected is a double-digit number is 16. Hence, option (c) is the correct answer.
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Consider S = (1, 2, 3,... 10). In how many ways two numbers from S can be selected so that the sum of the numbers selected is a double digit number?a)36b)16c)29d)9C2 - 5C2Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Consider S = (1, 2, 3,... 10). In how many ways two numbers from S can be selected so that the sum of the numbers selected is a double digit number?a)36b)16c)29d)9C2 - 5C2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider S = (1, 2, 3,... 10). In how many ways two numbers from S can be selected so that the sum of the numbers selected is a double digit number?a)36b)16c)29d)9C2 - 5C2Correct answer is option 'C'. Can you explain this answer?.
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