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The total number of 3 digit numbers which have two or more consecutive digits identical is:
a)171
b)170
c)90
d)180
Correct answer is option 'A'. Can you explain this answer?
a)171
b)170
c)90
d)180
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The total number of 3 digit numbers which have two or more consecutive...
For having maximum amount spent, the number of pens should be maximum i.e 15 pens
Total cost = 15 x 10 + 12 x 2 + 11 x 3
= Rs. 207
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
The total number of 3 digit numbers which have two or more consecutive...
Total Number of 3-Digit Numbers
To find the total number of 3-digit numbers that have two or more consecutive digits identical, we need to consider the different possibilities for the first digit, second digit, and third digit.
First Digit
The first digit of a 3-digit number can be any number from 1 to 9, except 0. So, there are 9 possibilities for the first digit.
Second Digit
The second digit can also be any number from 0 to 9. However, if the first digit is already chosen to be identical to the second digit, we have one less option. Therefore, there are 10 possibilities for the second digit if it is different from the first digit and 9 possibilities if it is the same.
Third Digit
Similarly, the third digit can also be any number from 0 to 9. However, if the second digit is already chosen to be identical to the third digit, we have one less option. Therefore, there are 10 possibilities for the third digit if it is different from the second digit and 9 possibilities if it is the same.
Total Number of Possibilities
To find the total number of 3-digit numbers, we need to multiply the number of possibilities for each digit together.
If the first digit is different from the second and third digits (9 possibilities), then the second digit can be chosen in 10 ways and the third digit in 10 ways as well. So, there are 9 * 10 * 10 = 900 possibilities in this case.
If the first digit is the same as the second digit (9 possibilities), then the second digit can be chosen in 9 ways (as it cannot be the same as the first digit) and the third digit in 10 ways. So, there are 9 * 9 * 10 = 810 possibilities in this case.
If the second digit is the same as the third digit (9 possibilities), then the second digit can be chosen in 10 ways and the third digit can be chosen in 9 ways (as it cannot be the same as the second digit). So, there are 9 * 10 * 9 = 810 possibilities in this case.
Total = 900 + 810 + 810 = 2520
However, we need to exclude the cases where all three digits are the same (e.g., 111, 222, etc.). There are 9 such numbers. So, the total number of 3-digit numbers with two or more consecutive digits identical is 2520 - 9 = 171.
Therefore, the correct answer is option A) 171.
To find the total number of 3-digit numbers that have two or more consecutive digits identical, we need to consider the different possibilities for the first digit, second digit, and third digit.
First Digit
The first digit of a 3-digit number can be any number from 1 to 9, except 0. So, there are 9 possibilities for the first digit.
Second Digit
The second digit can also be any number from 0 to 9. However, if the first digit is already chosen to be identical to the second digit, we have one less option. Therefore, there are 10 possibilities for the second digit if it is different from the first digit and 9 possibilities if it is the same.
Third Digit
Similarly, the third digit can also be any number from 0 to 9. However, if the second digit is already chosen to be identical to the third digit, we have one less option. Therefore, there are 10 possibilities for the third digit if it is different from the second digit and 9 possibilities if it is the same.
Total Number of Possibilities
To find the total number of 3-digit numbers, we need to multiply the number of possibilities for each digit together.
If the first digit is different from the second and third digits (9 possibilities), then the second digit can be chosen in 10 ways and the third digit in 10 ways as well. So, there are 9 * 10 * 10 = 900 possibilities in this case.
If the first digit is the same as the second digit (9 possibilities), then the second digit can be chosen in 9 ways (as it cannot be the same as the first digit) and the third digit in 10 ways. So, there are 9 * 9 * 10 = 810 possibilities in this case.
If the second digit is the same as the third digit (9 possibilities), then the second digit can be chosen in 10 ways and the third digit can be chosen in 9 ways (as it cannot be the same as the second digit). So, there are 9 * 10 * 9 = 810 possibilities in this case.
Total = 900 + 810 + 810 = 2520
However, we need to exclude the cases where all three digits are the same (e.g., 111, 222, etc.). There are 9 such numbers. So, the total number of 3-digit numbers with two or more consecutive digits identical is 2520 - 9 = 171.
Therefore, the correct answer is option A) 171.
Community Answer
The total number of 3 digit numbers which have two or more consecutive...
3(20)+2(20)+10(20)=300 So he can spend max 300 rs
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The total number of 3 digit numbers which have two or more consecutive digits identical is:a)171b)170c)90d)180Correct answer is option 'A'. Can you explain this answer?
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The total number of 3 digit numbers which have two or more consecutive digits identical is:a)171b)170c)90d)180Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The total number of 3 digit numbers which have two or more consecutive digits identical is:a)171b)170c)90d)180Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The total number of 3 digit numbers which have two or more consecutive digits identical is:a)171b)170c)90d)180Correct answer is option 'A'. Can you explain this answer?.
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