Combinatorics Question

Question

How many 6-character passwords can be created using the letters and numbers A, B, C, 1, 2, and 3 (each once) where the first character is a letter and the last character is a number?

Answer 1

Imagine 6 blank slots we must fill

_ _ _ _ _ _

The first slot must have a letter, there are 3 options for which letter to choose.

The last slot must be a number, there are 3 options for which number to choose.

After we choose a starting letter and an ending number, there are 4 characters left (2 letters and 2 numbers), which can be arranged in 4! ways.

3*3*4! = 216.