Question

How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when repetition of digits are allowed?

Answer 1

when repetation is a allowed
totally 0-5
so,
1-5,11-15,21-15,31-35,41-45,51-55=31
30 two digit numbers.
100-105,111-115,121-125,131-135,141-145,151-155,201-205,211-215,221-225,231-235,241-245,255.............500-505,511-515,521-525,531-535,541-545,551-555
Totally 185 numbers

Answer 2

Answer:

Total digit 216.

Step-by-step explanation:

Given : Digits 0,1,2,3,4,5

To find : How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when repetition of digits are allowed?

Solution :

We have three cases,

1. For 3 digit numbers :

Choose the first digit any of 5 ways. (can't be 0)

Choose the second digit any of 6 ways.

Choose the third digit any of 6 ways.

i.e, Total ways are (5)(6)(6) = 180

2.  2 digit numbers:

Choose the first digit any of 5 ways. (can't be 0)

Choose the second digit any of 6 ways.

i.e, (5)(6) = 30

3. 1-digit numbers :

Choose the first digit any of 5 ways.

i.e,  6 ways 0,1,2,3,4,5 =6

Total: 180+30+6 = 216