0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

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 times?

Solution
Verified by Toppr

There are $$5$$ one-digit natural numbers out of the given digits.

For getting $$2-digit$$ natural numbers we cannot put $$0$$ at the ten's place. So, this place can be filled by any of the given five nonzero digits in $$5$$ ways.

The unit's digit can be filled by any of the given six digits in $$6$$ ways.
So, the number of $$2-digit$$ natural numbers $$= (5\times 6) = 30$$.

Similarly, to get a $$3-digit$$ number, we cannot put on at the hundred's place. So, this place can be filled in $$5$$ ways, each of the ten's and unit's places can be filled in $$6$$ ways.

$$\therefore$$ the number of $$3-digit$$ numbers $$= (5\times 6\times 6) = 180$$.

Required number of numbers $$= (5 + 30 + 180) = 215$$.

Was this answer helpful?
5
Similar Questions
Q1

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 times ?

View Solution
Q2

How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times ?

View Solution
Q3
How many 4 digit numbers can be formed with digits 1,2,3,4,5 when digit may be repeated?
View Solution
Q4
How many 4digit numbers greater than 2300 can be formed with the digits 0,1,2,3,4,5 and 6, no digit being repeated in any number?
View Solution
Q5

How many three-digit numbers can be formed by using the digits 0,1,3,5,7 while each digit may be repeated any number of times?


View Solution