In: Statistics and Probability
A licence plate consists of seven symbols: digits or letters. How many license plates are there if the following is true:
(a) there must be three letters and four digits, and symbols may repeat?
(b) no restrictions on the quantity of letters and numbers, and symbols may repeat?
a) Here we require seven symbols on the number plate.
Given that number plate contains three letter and four digits. We know that there 10 digits and 26 letter or alphabets. We have to choose any 4 numbers from 10 and 3 alphabets from 26. And symbols may repetative.
Hence required number of plates are as follows :
. Thus totally 175760000 number plates can be made.
b) Here no restrictions on choosing the symbols for creating seven symbols number plate. And repetation also allowed here.
Hence we can choose the combinations of 2 whose addition is 7.
i.e. (1,6),(2,5),(3,4),(4,3),(5,2),(6,1). We have to choose both digits and letters simultaneously hence 0 can not be contain.
Hence the total number of number plates are as follows:
Thus total numbers of plates are 5003631360.