How many numbers between 1000 and 9999 do not have four different digits?
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Part (a) is correct, but (b) is not. You have solved the case where each digit of the number is odd, however, the question asks for odd numbers, which means only the last digit will be odd. Show
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jonroberts74 1890 Infinitum said: Part (a) is correct, but (b) is not. You have solved the case where each digit of the number is odd, however, the question asks for odd numbers, which means only the last digit will be odd.
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Infinitum 88140 Not quite. You already decided to reserve an odd digit for the units place, and you cannot have zero in the first digit. How many possibilities does that leave for the first digit? Apply the argument further to the second and third digits. Determine the number of numbers we can make between $1000$ and $9999$ of $4$ different digits without $0$. How many of those numbers are divisible by $3$? To calculate how many numbers there are between $1000$ and $9999$ of $4$ different digits without $0$ , we calculate $9*8*7*6=3024$. To calculate how many of those numbers are divisible by $3$ , I tried to combine that the sum of the digits must be divisible by $3$ and the stars and bars theorem. Since we have 4 different digits the maximum sum of the digits is $9+8+7+6=30$ and the minimum is $1+2+3+4=10$. The possible sums of the digits for which the number is divisible by $3$ are thus $12,15,18,21,24,27$ and $30$. But with the stars and bars I didn't really know how to do its because we have to have 4 different digits and no zeros. The solution my book gave was simply $42*4!$, so I think I'm on the wrong track, but I have no idea how they got to their solution. Any nudge in the right direction is appreciated :) EDIT I figured out the solution from my book. If we take the numbers 1 to 9 we can divide them in 3 sets mod 3. 0 mod 3 would be the numbers {3,6,9} 1 mod 3 would be the numbers {1,4,7} 2 mod 3 would be the numbers {2,5,8} Now we can use that the sum of the 4 digits must be $0$. We can take 1 number from the 0 mod 3 set and 3 from the 1 mod 3 set, for example 3147. There are 4! ways to use the numbers {3,4,1,7}. There are 3 ways to select 1 number from 0 mod 3 set and 3 from the 1 mod 3 set. Other ways to get a sum of 3: 2 numbers from the 0 mod 3 + 1 number from 2 mod 3+ 1 number from 1 mod 3. There are 3*3*3=27 ways to do this. 3 numbers from 2 mod 3+1 from 0 mod 3 . There are 3 ways to do this. 2 numbers from 1 mod 3 + 2 numbers from 2 mod 3. There are 3*3= 9 ways to do this. So there are 3+27+3+9=42 ways to get a 4 digit number with sum equal to 3, and we have 4! ways to rearrange those numbers, so 42*4! numbers between 1000 and 9999 comply with all the requirements. Number of natural numbers between 1000 and 9999 are (9999 – 1000 + 1) = 9000. How many integers from 1000 to 9999 have distinct digits?Hence, 4536 positive integers between 1000 and 9999 inclusive have distinct digits.How many four digit numbers are there from 1000 to 9999?The smallest 4-digit number is 1,000 and the largest 4-digit number is 9,999, and there are a total of 9000 numbers from 1000 to 9999.How many numbers in the range 1000 999 have no repeated digits?Hence, total 2296 numbers end in an even digit and have no repeated digits.How many numbers from 1000 to 9999 which do not contain four different digits?Solution : Total number=9000`9*9*8*7=4536` Number of numbers which do not have diffferent digit=`9000-4536=4464`. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Learn numbers from 1000 to 9999 | 4 digits | Class 2 | ICSE | CBSEHow many 4 digit palindromes are there?There are likewise 90 palindromic numbers with four digits (again, 9 choices for the first digit multiplied by ten choices for the second digit.How many possible 4 digit codes are there?There are 10,000 possible combinations that the digits 0-9 can be arranged into to form a four-digit code.How many possible 9 digit codes are there?Therefore, by multiplying the choices we have a total number of possibilities given by 9×9×8×7×6×5×4×3×2=3265920. Hence, 9 digit numbers of different digits can be formed in 3265920 ways.Which digit is missing in the average of numbers 9 99999 9999 999999999?Hence, the number does not contain zero digit. So, the correct answer is 0.How many numbers are there in the range from 10000 to 99999?Answer: The number of integers between 10,000 & 99,999 are 89,998. Number of integers between a & b including the numbers a & b is b - a + 1.What is the largest 4 digit number *?The largest 4 digit number is 9999.How many 7 digit numbers are there in all?Hence, answer is 90,00,000.How many odd integers between 1000 and 9999 including 1000 and 9999 whose digits are all different?Therefore, there are 2240 odd numbers in between 1000 and 9999 that have distinct digits .How many whole numbers are there between 999 and 9999?9000. (Nine Thousand). Was this answer helpful?What is the total number of numbers up to 9 999?From 0 to 9999 total whole number =9999+1=10,000.How many positive integers between 1000 and 9999 inclusive have distinct digits a 3000?Thus 4536 integers have distinct digits.How many numbers are there from 0000 to 9999?So 5040 different numbers can be made from 0000 to 9999 without repetitions.What are the 4 digit combinations 0 9 no repeats?So there are 4 x 3 x 2 x 1 = 24 possible ways of arranging 4 items. Therefore I divide 5040 / 24 = 210. So there are 210 different combinations of four digits chosen from 0-9 where the digits don't repeat.How many 9s are there between 1 and 99?Between 1 and 100, the digit 9 occurs in 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 and 99. ∴ The digit occurs 20 times between 1 and 100. Report Error Is there an error in this question or solution?How 9 is a magic number?The number 9 is revered in Hinduism and considered a complete, perfected and divine number because it represents the end of a cycle in the decimal system, which originated from the Indian subcontinent as early as 3000 BC.Does digit 9 occur between 1 and 100?There are total 20 nines between 1–100.How many combinations of 0 to 9 are there?In that case, each digit has 10 choices and there are 8 of them, so the answer is 108 = 100 000 000. When you use the word "combinations" it means something specific mathematically.How hard is it to crack a 4 digit code?You can crack more than 10 percent of random PINs by dialing in 1234. Expanding a bit, 1234, 0000, and 1111, make up about 20 percent. 26.83 percent of passwords can be cracked using the top 20 combinations.What is the rarest 4 digit code?Research suggests thieves can guess one in five PINs by trying just three combinations. How easy would it be for a thief to guess your four-digit PIN?How many 4 digit numbers are there between 1000 and 9999?The smallest 4-digit number is 1,000 and the largest 4-digit number is 9,999, and there are a total of 9000 numbers from 1000 to 9999.
How many whole numbers between 1000 and 9999 have distinct digits?Hence, 4536 positive integers between 1000 and 9999 inclusive have distinct digits.
How many odd numbers between 1000 and 9999 have distinct digits?Therefore, there are 2240 odd numbers in between 1000 and 9999 that have distinct digits .
How many integers from 1000 to 9999?How many integers are there from 1000 to 9999? Solution. The answer is 9999 − 1000 + 1 = 9000. Another way to think about it: They are the integers from 1 to 9000 with 999 added to each, so clearly there are 9000 of them.
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