# How many natural numbers less than 1000 can be formed from the digits 0,1,2,3,4,5 when a digit may be repeated any number of time?

Number of 1-digit numbers = 5 (0 can't be used)

Number of 2 digit numbers = 5 × 6 = 30 (0 can't be used at tens place)

Number of 3 digit numbers = 5 × 6 × 6 = 180 (0 can't be used at hundreds place)

∴Total numbers = 5 + 30 + 180 = 215

Cheers!!!

• 33

natural numbers less than 1000 means three digit numbers.

here you go....

options for units digit = 6

options for tens digit = 6 .......(repetition allowed)

options for hundredth digit = 6-1 = 5 .......(0 can't be the first digit)

thus the answer is, 6*6*5 = 180.

• -10

one digit numbers= 5

natural numbers less than 1000 means one digit, two digit or three digit numbers.

two digit numbers = 5*6=30  (0 not allowed )

three digit numbers:-

options for units digit = 6

options for tens digit = 6 .......(repetition allowed)

options for hundredth digit = 6-1 = 5 .......(0 can 't be the first digit)

total three digit numbers=6*6*5=180.

thus, the final answer is 5+30+180

= 215.

hope its roght, thumbs up please.

thus the answer is, 6*6*5 = 180.numbers :-

• 2

5+5*6+5*6*6

=5+30+180

=215

• -10
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