Find the number of numbers of $5$ digits that can be formed with the digits $0, 1, 2, 3, 4$ if the digits can be repeated in the same number.

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Solution

In a five digit number $0$ cannot be put in ten thousand’s place. So, the number of ways of filling up the ten thousand’s place $= 4$ .
Since the repetition of digits is allowed, therefore each of the other places can be filled in $5$ ways.
So, the required number of numbers $= 4 \times 5 \times 5 \times 5 \times 5 = 2500.$

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Find the number of numbers of 5 digits that can be formed with the digits 0,1,2,3,4 if the digits can be repeated in the same number.

In a five digit number 0 cannot be put in ten thousand’s place. So, the number of ways of filling up the ten thousand’s place =4.Since the repetition of digits is allowed, therefore each of the other places can be filled in 5 ways.So, the required number of numbers =4×5×5×5×5=2500.

Find the number of numbers of $5$ digits that can be formed with the digits $0, 1, 2, 3, 4$ if the digits can be repeated in the same number.