How many codes are there that have 3 letters and 2 numbers? - Answers

There are 26 different letters.There are 10 different numbers.If a letter or number is allowed to repeat in the code:Number of ways to make 3 letters = 26 x 26 x 26 = 17,576Number of ways to make 2 numbers = 10 x 10 = 100Number of ways to make 3 letters and 2 numbers = 17,576 x 100 = 1,757,600Each group of 3 letters and 2 numbers can be arranged in (5 x 4 x 3 x 2) = 120 different ways.So the number of different codes = 1,757,600 x 120 = 210,912,000 .If a letter or number is not allowed to repeat in the code:Number of ways to make 3 letters = 26 x 25 x 24 = 15,600Number of ways to make 2 numbers = 10 x 9 = 90Number of ways to make 3 letters and 2 numbers = 15,600 x 90 = 1,404,000Each group of 3 letters and 2 numbers can be arranged in (5 x 4 x 3 x 2) = 120 different ways.So the number of different codes = 1,404,000 x 120 = 168,480,000 .