The digit 0,1,2,3,4 can make how many natural numbers that is less than 1,000
Answers
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
Given : The digit 0,1,2,3,4
To find : how many natural numbers that is less than 1,000 using the Digits
Solution:
Case 1 : Lets consider no repetition of digit
1 Digit numbers - 4 ( 1 - 4)
2 Digit numbers 1st Digit can be in 4 Ways 2nd Digit can be in 4 ways
= 4 * 4 = 16
3 Digit Numbers - 1st Digit can be in 4 Ways , 2nd Digit can be in 4 ways , 3rd digit can be in 3 Ways
= 4 * 4 * 3
= 48
Hence total = 4 + 16 + 48 = 68
68 Natural Numbers less than 1000 with The digit 0,1,2,3,4 when no repetition of Digits
Case 2 : Lets consider repetition of digit
1 Digit numbers - 4 ( 1 - 4)
2 Digit numbers 1st Digit can be in 4 Ways 2nd Digit can be in 5 ways
= 4 * 5 = 20
3 Digit Numbers - 1st Digit can be in 4 Ways , 2nd Digit can be in 5 ways , 3rd digit can be in 5 Ways
= 4 * 5 * 5 = 100
Hence Total = 4 + 20 + 100 = 124
Hence 124 Natural number less than 1000 with The digit 0,1,2,3,4 when repetition of Digits
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