Question

If a license plate has 3 letters and then 3 numbers, what are the chances (probability?) of getting at least 1 letter "Z" in one of the letter spots if the letters are picked randomly?
and I think each letter can only be used once.

Answer 1

when you say, "at least 1 letter "Z" in one of the letter spots", you are implying that there could be 1,2, or 3 Z's in the letter spots.
But then you say that you think each letter can be used only once.

Usually on license plates, letters and numbers can be repeated, so I will work it out assuming that both letters and numbers can be repeated.

case 1: one Z
number of ways = 3x25x25x1000 = 1875000
case 2: two Z's
number of ways = 3x25x1000 = 75000
case 3: three Z's
number of ways = 1x1000 = 1000
total number of ways to have Z's = 1951000

number of ways without restrictions = 26x26x26x1000 = 17576000

<b>so prob of at least 1 Z = 1951000/17576000 = ..111</b>

other way:
no Z's at all = 25x25x25x1000 = 15625000
so number of ways for at least one Z
= 17576000 - 15625000 = 1951000
etc.