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  • How many five-digit number license plates can be made if (i) first digit cannot be zero and the repetition of digits is not allowed. (ii) the first digit cannot be zero, but the repetition of digits is allowed?

How many five-digit number license plates can be made if (i) first digit cannot be zero and the repetition of digits is not allowed. (ii) the first digit cannot be zero, but the repetition of digits is allowed?

Answers (1)

(1)

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 x 9 x 8 x 7 x 6=27216

(2)

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 =10 (since repetition is allowed)
Number of ways of filling the third digit =10
Number of ways of filling the fourth digit =10
Number of ways of filling the fifth digit =10
Total number of licence plates that can be made =9 x 10 x 10 x 10 x 10= 90,000

Posted by

shubham.krishnan

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