Question

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?

Answer 1

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.