# How Many Different Five-digit Number Licence Plates Can Be Made Iffirst Digit Cannot Be Zero and the Repetition of Digits is Not Allowed, - Mathematics

How many different five-digit number licence plates can be made if

first digit cannot be zero and the repetition of digits is not allowed,

#### Solution

(i) Since the first digit cannot be zero, the number of ways of filling the first digit = 9
Number of ways of filling the second digit = 9     (Since repetition is not allowed)
Number of ways of filling the third digit = 8
Number of ways of filling the fourth digit = 7
Number of ways of filling the fifth digit = 6
Total number of licence plates that can be made = 9$\times$9$\times$8$\times$7$\times$6 = 27216

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 19.1 | Page 15