Posted by **Diane** on Sunday, September 20, 2009 at 10:57am.

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.

- Math -
**Reiny**, Sunday, September 20, 2009 at 11:29am
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

**so prob of at least 1 Z = 1951000/17576000 = ..111**

other way:

no Z's at all = 25x25x25x1000 = 15625000

so number of ways for at least one Z

= 17576000 - 15625000 = 1951000

etc.

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