Question

In: Statistics and Probability

A licence plate consists of seven symbols: digits or letters. How many licence plates are there...

A licence plate consists of seven symbols: digits or letters. How many licence plates are there if the following is true:

(1) there must be three letters and four digits, and symbols may repeat?

(2) no restrictions on the quantity of letters and numbers, and symbols may repeat?

Expert Solution

Please note

Also, by the rule of permutations, the number of arrangements of n things, all taken together (repetition allowed) = nⁿ.

There are 26 (A - Z) letters and 10 single unit digits (0 - 9)

There is no restriction on the place of the symbols and repetition is allowed.

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(1) Choose 3 letters from 26 in 26C3 = 2600 ways

Choose 4 digits in 10C4 = 210 ways

These 7 chosen symbols can be arranged in 7⁷ ways.

Therefore Total Number of license plates = 2600 * 210 * 7⁷ = 4.49654 * 10¹¹.

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(2) No restrictions on quantity. Therefore total possible options = 26 letters + 10 digits = 36

Therefore each of the 7 positions can hold any of these 36 symbol.

Therefore total number of arrangements = 36⁷ = 78,364,164,096

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orchestra answered 2 years ago

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