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
a.
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
b.
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 1 year agoRelated Solutions
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