How many numbers are there between 100 and 500 with the digits 0, 1, 2

1.	How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5 if(i) repetition of digits allowed(ii) the repetition of digits is not allowed
Answer» (i) The given digits are 0, 1, 2, 3, 4, 5 We have to find numbers between 100 and 500. So the 100’s place can be filled (by the numbers 1, 2, 3, 4) in 4 ways. The 10’s place can be filled in (using 0, 1, 2, 3, 4, 5) 6 ways and the unit-place can be filled in (using 0,1, 2, 3, 4, 5) 6 ways But the number 100 should be excluded So the number of numbers between 100 and 500 = 4 × 6 × 6 = 144 (ii) The 100’s place can be filled (by using 1, 2, 3, 4) 10’s in 4 ways The 10’s place can be filled in (6 – 1) 5 ways and the unit place can be filled in (5 – 1) 4 ways So the number of 3 digit number 4 × 5 × 4 = 80

How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5 if(i) repetition of digits allowed(ii) the repetition of digits is not allowed

Answer»

(i) The given digits are 0, 1, 2, 3, 4, 5

We have to find numbers between 100 and 500. So the 100’s place can be filled (by the numbers 1, 2, 3, 4) in 4 ways.

The 10’s place can be filled in (using 0, 1, 2, 3, 4, 5) 6 ways and the unit-place can be filled in (using 0,1, 2, 3, 4, 5) 6 ways

But the number 100 should be excluded

So the number of numbers between 100 and 500 = 4 × 6 × 6 = 144

(ii) The 100’s place can be filled (by using 1, 2, 3, 4) 10’s in 4 ways

The 10’s place can be filled in (6 – 1) 5 ways and the unit place can be filled in (5 – 1) 4 ways

So the number of 3 digit number 4 × 5 × 4 = 80