How many different five-digit number licence 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?
(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 $=9 \times 9 \times 8 \times 7 \times 6=27216$
(ii) 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 $=9 \times 10 \times 10 \times 10 \times 10=90000$
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