Question

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 1

Step-by-step explanation:

ANSWER

Digits are 0,1,2,3,4,5

Between 100 and 500

i) Repetition allowed

0,5 can not be at the hundredth place

100 is to be excluded

so the total number of numbers can be formed =6×6×4−1=143

ii) Repetition not allowed

Hundredth place =4

Tenth place =5

Once place =4

Total =4×5×4=80

Answer 2

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$\Large\bold\blue{Question}$

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

$\Large\bold\blue{Solution}$

i) Repetition of digits allowed

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 repetition of digits is not allowed

$\Large\bold\blue{Solution}$

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

$\Large\fbox\red{Mark \:As\:Brainliest}$