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How many 5 digit palindromes are there?
900 This explains it. A positive integer is a palindrome if it reads the same forward and backwards such as 1287821 and 4554. Determine the number of 5-digit positive integers which are NOT palindromes. We start by counting the total number of 5 digit positive integers. The first digit is between 1 and 9, so we have 9 choices. Each of the other 4 digits can be anything at all (10 choices for each). This gives us 9(10)4 = 90000 five-digit positive integers. Now we need to count the number of 5 digit palindromes. Again, we have 9 choices for the first digit and 10 choices for each of the next two. The tens and units digits however are fixed by our choices so far. Therefore, there are only 900 five-digit palindromes. Therefore, the total number of five-digit positive integers which are not palindromes is 90000-900 = 89100.
How many three-digit positive integers have digits whose product is 24?
To find the number of three-digit positive integers with digits whose product is 24, we can break down 24 into its prime factors: 2 x 2 x 2 x 3. The possible combinations for the three digits are (2, 2, 6), (2, 3, 4), and (2, 4, 3). These can be arranged in 3! ways each, giving a total of 3 x 3! = 18 three-digit positive integers.
How many different products are possible when two one-digit positive integers are multiplied?
When two one-digit positive integers are multiplied, there are a total of 81 different products possible. This is because there are 9 possible choices for the first digit (1-9) and 9 possible choices for the second digit (1-9), resulting in 9 x 9 = 81 possible combinations.
What are distinct positive integers?
The set of positive integers is {1,2,3,4,5,...}. When referring to numbers, distinct simply means different from each other e.g. 2,6,7 and 9 are distinct positive integers but 2,6,6 and 9 are not distinct since two of them are equal.
How many different two-digit numbers can be written if each digit must be one of the integers from 1 to 8 inclusive?
There are 8*8 = 64 such numbers.
