College probability and statistics

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The current license plates in New York State consist of three letters followed by four digits.
( i ) How many possible distinct license plates can there be?
( ii ) How many possible distinct license plates could there be if the letters O and I and the digits, 0 and 1 were prohibited because they look alike?
( iii ) How many different license plates are there that have precisely two C's and two 2's? (Here we are no longer prohibiting O's, I's, 0's and 1's.) [Hint: Consider placing the two C's in position and then filling in the other letter. Do something similar with the digits

  • College probability and statistics -

    3 letters ---> 26^3
    3 numbers, assuming it may start with a zero
    --- 10^4

    number of plates = 26^3 (10^4) = 175760000

    (about 176 million, long way to go)


    ii) so only 24 letters, and 8 numbers
    -- what do you think?

    iii) look at the letter part first:
    assume we put CC at the front
    so number of such cases = 1x1x25x25 = 625
    CCMP could be one those, but each one can be arranged in 4!/2! or 12 ways
    the letters can be arranged in 625x12 or 7500 ways
    using the same argument for the numbers, there are
    1x1x9x9 x 12 ways or 972 ways
    number of ways according to the stated conditions
    = 7500x972 = 7290000 ways

  • College probability and statistics -

    8585

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