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

Answer 1

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 = 17,576

Number of ways to make 2 numbers = 10 x 10 = 100

Number of ways to make 3 letters and 2 numbers = 17,576 x 100 = 1,757,600

Each 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 = 15,600

Number of ways to make 2 numbers = 10 x 9 = 90

Number of ways to make 3 letters and 2 numbers = 15,600 x 90 = 1,404,000

Each 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 .