Question

In: Math

An automobile license plate consists of 3 letters followed by 4 digits. How many different plates...

An automobile license plate consists of 3 letters followed by 4 digits. How many different plates can be made:

a. If repetitions are allowed?

b. If repetitions are not allowed in the letters but are allowed in the digits?

c. If repetitions are allowed in the letters but not in the digits?

Solutions

Expert Solution

3 letters followed by 4 digits

Total number of letters = 26

Total number of digits = 10

Total = 7

If repetitions are allowed?

3 letters out of 26 and 4 digits out of 10 and repetitions are allowed

Total number of cases in letters = 26^3 = 17576

Total number of cases in digits = 10^4 = 10000

Total number of cases = Total number of cases in letters*Total number of cases in digits

Total number of cases = 17576*10000

Total number of cases = 175760000

If repetitions are not allowed in the letters but are allowed in the digits?

Total number of cases in digits = 10^4 = 10000 ( repetition allowed )

Total number of cases in letters = 26P3 ( repetition not allowed and order does matter )

Total number of cases in letters = 26!/(26-3)!

Total number of cases in letters = 26!/23!

Total number of cases in letters = 26*25*24

Total number of cases in letters = 15600

Total number of cases = Total number of cases in letters*Total number of cases in digits

Total number of cases = 15600*10000

Total number of cases = 156000000

c. If repetitions are allowed in the letters but not in the digits?

Total number of cases in letters = 26^3 = 17576 ( repetition allowed )

Total number of cases in digits = 10P4 ( repetition not allowed and order does matter )

Total number of cases in digits = 10!/(10-4)!

Total number of cases in digits = 10!/6!

Total number of cases in digits = 10*9*8*7

Total number of cases in digits = 5040

Total number of cases = Total number of cases in letters*Total number of cases in digits

Total number of cases = 17576*5040

Total number of cases = 88583040

milcah answered 7 months ago

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