how many numbers from 1 to 2000 have none of their digits repeated?
Answers
Answer:
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Answer:
Total numbers from 1 to 2000 have none of their digits repeated = 1243
Step-by-step explanation:
To find,
The total count of numbers from 1 to 2000, with none of their digits repeated
Solution:
Number of one-digit numbers between and 1 to 2000 = 9
Number of two-digit numbers between and 1 to 2000
Number of possible digits in tens place = 9, (digit '0' is not possible)
Number of possible digits in ones place = 9, (9 digits including '0' and excluding the digit in the tens place)
Total possible two-digit numbers are = 9×9 = 81
Number of three-digit numbers between and 1 to 2000
Number of possible digits in hundred's place = 9, (digit '0' is not possible)
Number of possible digits in tens place = 9, (9 digits including '0' and excluding the digit in the hundreds place)
Number of possible digits in ones place = 8, (excluding the digits in hundreds and tens place)
The total possible three-digit numbers = 9×9×8 = 648
Number of four-digit numbers between and 1 to 2000
Number of possible digits in the thousand's place = 1(only digit 1 is possible)
Number of possible digits in hundred's place = 9, (all digits including '0' and excluding '1')
Number of possible digits in tens place = 8, (excluding the digits in hundreds and tens place)
Number of possible digits in ones place = 7, (excluding the digits in hundreds, tens place and one's place)
The total possible four-digit numbers are 9×8×7×1 = 504
Four-digit numbers when 2000 is included = 505
Total possible numbers are 505+648+81+9 = 1243
Total numbers from 1 to 2000 have none of their digits repeated = 1243
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