108,117,126,135,144,153,162.
171, 180
It is 120 if the digits cannot be repeated.
108 117 126 135 144 153 and 162
In the numbers 1-9 each number has 1 digit and there are 9 of them, so that's 9.In 10-99 each number has 2 digits, and there are 90 of them: 2x90 = 180There are 900 three digit numbers [100 through 999]: 2700 digits.There are 9000 four digit numbers: 36000 digits.90,000 numbers with five digits: 450,000 digits.900,000 numbers with six digits: 5,400,000 digits.Then 1 number with seven digits: 7 digits.Add them up and you have 5,888,896 digits.
Total possible 4-digit numbers= 1000, 1001,...,9999 = 9000 Total with same digit numbers = 1111,2222,...,9999 = 9 9000 - 9 = 8991
5 digit telephone numbers having at least one of their digits repeated is = total possible 5 digit telephone numbers - 5 digit telephone numbers without any digit being repeated. =(10*10*10*10*10)-(10*9*8*7*6) =100000-30240 =69760
It is 120 if the digits cannot be repeated.
108 117 126 135 144 153 and 162
In the numbers 1-9 each number has 1 digit and there are 9 of them, so that's 9.In 10-99 each number has 2 digits, and there are 90 of them: 2x90 = 180There are 900 three digit numbers [100 through 999]: 2700 digits.There are 9000 four digit numbers: 36000 digits.90,000 numbers with five digits: 450,000 digits.900,000 numbers with six digits: 5,400,000 digits.Then 1 number with seven digits: 7 digits.Add them up and you have 5,888,896 digits.
24 three digit numbers if repetition of digits is not allowed. 4P3 = 24.If repetition of digits is allowed then we have:For 3 repetitions, 4 three digit numbers.For 2 repetitions, 36 three digit numbers.So we have a total of 64 three digit numbers if repetition of digits is allowed.
All two digit numbers which the digits add up to 11 are :- 29, 38, 47, 56, 65, 74, 83 & 92.
Total possible 4-digit numbers= 1000, 1001,...,9999 = 9000 Total with same digit numbers = 1111,2222,...,9999 = 9 9000 - 9 = 8991
5 digit telephone numbers having at least one of their digits repeated is = total possible 5 digit telephone numbers - 5 digit telephone numbers without any digit being repeated. =(10*10*10*10*10)-(10*9*8*7*6) =100000-30240 =69760
There are seven possible digits for the first digit and 6 digits for the second (minus one digit for the digit used as the first digit) and 5 options for the last digit (minus one again for the second digit) and then you just multiply them all together to get a total possible combination of 210 numbers that are possible.
I suggest you calculate (1) how many numbers are in total, and (2) how many numbers in that range do NOT have 6 as a digit. Then you can subtract the result of (1) minus the result of (2).
There are 2000 possible five digit numbers that can be formed from the digits 02345 that are divisible by 2 or 5 or both. To be divisible by 2, the last digit must be even, namely 0, 2 or 4 (in the digits allowed). To be divisible by 5, the last digit must be 0 or 5. Thus to be divisible by 2 or 5 or both, the last digit must be 0, 2, 4 or 5 (a choice of 4). Presuming that a 5 digit number must be at least 10000, then: For the first digit there is a choice of 4 digits (2345); for each of these there is a choice of 5 digits (02345) for the second, making a total so far of 4 x 5 numbers; for each of these choices for the first and second digits there is a choice of 5 digits (02345) for the third digit making the total so far (4 x 5) x 5 numbers; for each of these choices for the first three digits there is a choice of 5 digits (02345) for the fourth digit making the total so far (4 x 5 x 5) x 5 numbers; for each of these choices for the first four digits there is a choice of 4 digits (0245 - as discussed above) for the last digit, giving a total of (4 x 5 x 5 x 5) x 4 numbers. So the total number of five digit numbers so formed is: number = 4 x 5 x 5 x 5 x 4 = 2000.
90000. With 10 digit palindromes, the last 5 digits are the same as the first 5 digits in reverse, eg 12345 54321. So it comes down to how many 5 digit numbers are there? They are the numbers "10000" to "99999", a total of 99999 - 10000 + 1 = 90000.
48. Assuming no digit can be used more than once, the two digit numbers divisible by 4 are: 16, 36, 48, 56, 64, 68, 84, 96 8 of them. For any number to be divisible by 4, only the last two digits need be divisible by 4; so for three digit numbers, each of the two digit numbers above can be preceded by any of the remaining 5 digits and still be divisible by 4. → 5 x 8 = 40 three digit numbers are divisible by 4 → 40 + 8 = 48 two or three digit numbers made up of the digits {1, 3, 4, 5, 6, 8, 9} are divisible by 4. If repeats are allowed, there are an extra 2 two digit numbers (44 and 88) and each of the two digit numbers can be preceded by any of the 7 digits, making a total of 7 x 10 + 10 = 80 two and three digits numbers divisible by 4 make up of digits from the given set.