Stratton K.

asked • 01/03/21

Probability question

Q: How many different license plates can be formed if each plate has 5 different digits followed by 1 letter?

Philip P.

If the digits all have to be different (no repeats of a numeral), then it would be 10 x 9 x 8 x 7 x 6 x 26. Otherwise 10^5 x 26 is correct.
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01/03/21

1 Expert Answer

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Benjamin H. answered • 01/03/21

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There are ten digits possible, with none being repeated, and 26 letters possible, so we know that the answer would be P(10,5) * 26 = 786,240


P(10,5) is a permutation which selects five numbers without replacement.


Thanks to Tom K. for the correction

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Mark H.

correct!!!
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01/03/21

Tom K.

It says 5 different digits. It should be P(10,5)*26 = 786240
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01/03/21

Theodore H.

Tom is correct. 10^5 allows numbers to be repeated, whereas permutations P(10,5) selects the five numbers without replacement (i.e., no repeats) AND counts the number of distinct ways that these five numbers can be arranged.
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01/03/21

Wendy D.

tutor
As a beginning student, it helps to look at this problem like this: 10(possibilities for 1st position) * 9 (possibilities for 2nd position) * 8 (possibilities for 3rd position) * 7 (possibilities for 4th position) * 6 (possibilities for 5th position) * 26 (possibilities for 6th position)
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01/05/21

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