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PA license plates have 3 letters followed by 4 numbers a. If the same letter or number can be repeated, how many can be made? b. If the same letter CANNOT be repeated, how many can be made
PA license plates have 3 letters followed by 4 numbers a. If the same letter or number can be repeated, how many can be made? b. If the same letter CANNOT be repeated, how many can be made
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Answer:
26
3
×
10
4
=
175
,
760
,
000
plates
Explanation:
There are 3 spots where there are 26 choices each
(
=
26
3
)
and 4 spots where there are 10 choices each (the digits 0 through 9,
=
10
4
). This gives:
26
3
×
10
4
=
175
,
760
,
000
plates
~~~~~
In response to a comment, here's some more information:
If the same letter can't be repeated, we can look at things this way. The first letter spot can be any one of the 26 letters. The second letter spot can be any one of the remaining 25 letters. And the third letter spot can be any one of the remaining 24 letters. This gives, for letters:
26
×
25
×
24
=
15600
(note - this is the same as a permutation with population 26 and picking 3)
We still have
10
4
for the numbers, and so in total we have:
15600
×
10000
=
156
,
000
,
000
plates