How many ways can you make a 5-letter passcode using the digits a, b, c, d, e, f, g, h, i, j if repetition of letters is not allowed?

You can use the letters: a, b, c, d, e, f, g, h, i, and j to make a 5-letter passcode. So you have 10 letters.

For the 1st place you can use 10 letters, for the 2nd you can use 9 (because the repetition of letters is not allowed) and so on.

Therefore: 10 * 9 * 8 * 7 * 6 = 30,240

It is also known as a variation of m elements choose n (V m, n):

V (10, 5) = m * (m - 1) * ... * (m - n + 1) = 10 * 9 * 8 * 7 * 6 = 30,240

Answer: You can make a passcode in 30,240 ways.