A certain state has license plates showing three numbers and three letters. How many different license plates are possible (a) if the numbers must come before the letters? (b) if there is no restriction on where the letters and numbers appear? There are 10 possible digits for the numbers (0 to 9) and 26 possible letters (A to Z)
n<-10*10*10 #the numbers
l<-26*26*26 #the letters
n## [1] 1000l## [1] 17576t<-n*l
t## [1] 17576000The number of different license plates is 17576000 if the numbers are followed by the letters (b) 6C3
c<-(factorial(6))/((factorial(6-3))*(factorial(3)))
l<-t*c
l## [1] 351520000The number of different license plate is 351520000