# SOLUTION: how many 4-digit numbers can be formed with the 10 digits 0,1,2,3...9 of (a)repetitions are allowed,(b)not allowed,(c) the last digit must be 0 and repetitions are not allowed

Algebra ->  Permutations -> SOLUTION: how many 4-digit numbers can be formed with the 10 digits 0,1,2,3...9 of (a)repetitions are allowed,(b)not allowed,(c) the last digit must be 0 and repetitions are not allowed      Log On

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 Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Permutations Question 524252: how many 4-digit numbers can be formed with the 10 digits 0,1,2,3...9 of (a)repetitions are allowed,(b)not allowed,(c) the last digit must be 0 and repetitions are not allowedAnswer by Edwin McCravy(9716)   (Show Source): You can put this solution on YOUR website!how many 4-digit numbers can be formed with the 10 digits 0,1,2,3...9 of (a)repetitions are allowed, ```Two ways to get the answer: 1. There are 9999 integers starting with 1 and ending with 9999. But the 999 integers starting with 1 and ending with 999 have less than 4 digits, so the desired number is 9999-999 or 9000 ways. 2. There are 9 ways to pick the first digit (1 through 9), there are 10 ways to pick the 2nd, 3rd, and 4th digits, so that 9×10×10×10 = 9000 ways. ``` (b)not allowed, ```There are 9 ways to pick the first digit (it can't be 0), 9 ways to pick the 2nd digit (it can be 0, just not what we picked for the 1st digit), 8 ways to pick the third digit, and 7 ways to pick the fourth digit. That's 9×9×8×7, or 4536 ways. ``` (c) the last digit must be 0 and repetitions are not allowed: ```We can choose the first digit any of 9 ways, the second digit any of 8 ways, the third digit any of 7 ways and the last digit only 1 way (a 0). That's 9×8×7×1 = 504 ways. Edwin```