How many numbers lying between 100 and 1000 can be formed with the digits 0,1,2,3,4,5, if the repetition of the digits is not allowed?

Question

Answer

Answer is 100

see how

The number will be a

3

digit number

Let us consider the

3

digits to be

3

boxes

□

in which the numbers can be placed.

First box can be filled in

5

ways(

1

,

2

,

3

,

4

,

5

)

Second box can be filled in

5

ways(

0

,or any

4

of (

1

,

2

,

3

,

4

,

5

) )

Third box can be filled up in

4

ways( The

4

numbers unused in the first

2

boxes)

Therefore, total number of ways=

5

⋅

5

⋅

4

=

100

Answer

Answer

(Just trying some other method as the best method is already posted)

Any three digit number is of the form ABC. A cannot be zero so it can be filled in 5 ways and the rest B,C can be filled in 6 ways. So, total number of numbers possible = 5 x 6 x 6 = 180 numbers

There are 5 number (111,222,333,444,555) where all are three digits are repeated.

Any three digit number where two are repeated is of the forms AAB, ABA, BAA. In any case the first digit must not be zero (= 5 ways) and the next one can be any digit except the first (= 5 ways). So there are a total of 3 x 5 x 5 = 75 numbers where two digits are repeated.

Total number of words with no repetition = 180 - 75 - 5 = 100 numbers

Answer

Ek jbab the amswer is 100

Answer

**Counting the Numbers**

To determine the number of numbers that can be formed between 100 and 1000 using the digits 0, 1, 2, 3, 4, and 5, without repetition, we need to consider the following:

1. **Number of choices for the hundreds place:** Since the number should be greater than 100, the hundreds place cannot be zero. Therefore, we have 5 choices (1, 2, 3, 4, or 5) for the hundreds place.

2. **Number of choices for the tens place:** After selecting a digit for the hundreds place, we have one less digit available to choose for the tens place. So, we have 5 choices for the tens place.

3. **Number of choices for the units place:** Similarly, after selecting digits for the hundreds and tens places, we have two fewer digits available to choose from for the units place. Hence, we have 4 choices for the units place.

4. **Total number of numbers:** To obtain the total number of numbers, we multiply the number of choices for each place value together:

Number of choices for hundreds place * Number of choices for tens place * Number of choices for units place = 5 * 5 * 4 = 100

Therefore, there are 100 numbers between 100 and 1000 that can be formed using the digits 0, 1, 2, 3, 4, and 5 without repetition.

Similar Class 11 Doubts

how many numbers greater than 1000 but not greater than 4000 can be formed with the digits 0,1,2,3,4 . if a. repetition is allowed. b. repetition is not allowed

How many different numbers between 100 and 1000 can be formed using the digits 0 1 2 3 4 5 6 assuming that in any numbers the digit are not repeated also find how many of these will be divisible by 5 ?

How many 3 digit even numbers can be form from digits 1, 2 , 3 , 4 , 5 , 6 if the digits can be repeated ?

Number of 5 digit numbers divisible by 25 that can be formed using only the digits 1,2,3,4,5 & 0 taken five at a time

How many numbers greater than 24000 can be formed by using digits 1,2,3,4,5 when no digit is repeated?

Top Courses for Class 11View all

Chemistry Class 11

CUET Mock Test Series

English Class 11

Chemistry Practice Tests: CUET Preparation

CUET Mock Test: Humanities Subjects 2025

Top Courses for Class 11

Top Courses for Class 11

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams