Postal Letter

How many ways can you create a postal code?

How many ways can a postal code be made if the postal code must be letter, number, letter, number, letter. 1. Numbers and letters can not be repeated 2. The postal code can not start with the letter O and the numbers can not be repeated

Public Comments

1. Let's start with a simpler problem. Say you had 4 different numbers and 6 different letters to create apartment numbers. The question is how many different apartment numbers are there? Think...each number has 6 different letters that it could be assigned to, right? Meaning, there are 6 apartment numbers. If there are 4 numbers then there are 4 times as many apartment numbers. So there are (4)(6) possible apartment numbers or 24 possibilities! Here you just multiplied the two different possibilities, 4 different numbers and 6 different letters, together. That is what you have to do for your problem. First decide how many blanks are in the postal code. If the code must be letter, number, letter, number, letter, that is five blanks regardless of whether it is a number or letter. Write: _ _ _ _ _ because there are five blanks (this helps to visualize the code). For the first blank, you must have a letter, but not O. How many possible letters can fit on the first blank?... there are 26 letters in the alphabet and O cannot be it...so 26 - 1 = 25...which equals 25 possibilities for the first blank. Lets write that in. 25 _ _ _ _ (the other four possibilities still have to be calculated) For the second blank, you must have a number. (When the question is saying number, I am assuming either 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) Since there are 10 possible numbers that can fit in the second blank, write a 10 in the second blank. 25 10 _ _ _ (the other three possibilities still have to be calculated) For the third blank, you must have a letter, but not one already written and it CAN be O. Since there are 26 letters in the alphabet, (O can now be used ) one cannot be used because it was already written down...26 - 1 = 25. There are again 25 possibilities for the third blank. 25 10 25 _ _ (the other two possibilities still have to be calculated) For the fourth blank, you must have a number, but not one already written. Since there were 10 possible digits that could be used, and one was already used...10 - 1 = 9...there are 9 possibilities for the fourth blank. 25 10 25 9 _ (the last possibility still has to be calculated) For the last blank, you must have a letter, but not one already written. Since there are 26 letters in the alphabet, and 2 of them were already written...26 - 2 = 24...there are 24 possibilities for last blank! 25 10 25 9 24 Now!...just like you multiplied all the possibilities of numbers and letters in the beginning problem, in your problem you do the same! The possibilities are 25, 10, 25, 9, and 24. Multiply all of these together to get your answer! (25)(10)(25)(9)(24) = 1,350,000 possible ways the postal code could be be made! Hope that helps!