How many 3 digit numbers can be formed using the digits 1 2 3 4 5 if digits can be repeated? ✅ 2023

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How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that:1) Repetition is not allowed.2) Repetition is allowed. How many 3 digit numbers can be formed with the digits 1 2 3 4 and 5 which are divisible by 5 and in which the digits are not repeated?What is the value of a 3 digit number?How are three digit numbers formed in math?Ex 7.1, 1 (i) - Chapter 7 Class 11 Permutations and Combinations (Term 2)How many ways can a 3How many 3 numbers can be formed from the digits 1 2 3 4 and assuming that I repetition of the digits is allowed II repetition of the digits is not allowed?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that:1) Repetition is not allowed.2) Repetition is allowed.

Answer

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Hint: Fundamental principle of counting: According to the fundamental principle of counting if a task can be done in “m” ways and another task can be done in “n” ways, then the number of ways in which both the tasks can be done in mn ways.

Complete step by step solution:
Case [1]: Repetition not allowed:
The number of ways in which the ones place can be filled = 5 ways.
The number of ways in which the tens place can be filled = 4 ways (because repetition is not allowed. So, the choice of one place cannot be used).
 The number of ways in which hundreds place can be filled = 3 ways.
Hence according to the fundamental principle of counting the number of ways in which the three places can be filled to form a three-digit number = $5times 4times 3=60$
Hence the number of 3-digit numbers formed using the digits 1, 2, 3, 4 and 5 = 60 i.e 5! ways
Case [2]: Repetition is allowed:
The number of ways in which the ones place can be filled = 5 ways.
The number of ways in which the tens place can be filled = 5 ways (because repetition is allowed. So, the choice of one's place can be used).
 The number of ways in which hundreds place can be filled = 5 ways.
Hence according to the fundamental principle of counting the number of ways in which the three places can be filled to form a three-digit number = $5times 5times 5=125$
Hence the number of 3-digit numbers formed using the digits 1, 2, 3, 4 and 5 = 125

Note: The number of 3-digit numbers formed using the digits 1, 2, 3, 4 and 5 when repetition is not allowed is equivalent to the number of 3 Letter permutations of 5 distinct letter = $^5P_3=dfrac5!left( 5-3 right)!=dfrac5!2!=dfrac1202=60$ which is the same result as above.

Table of Contents

1 How many different 3 digit numbers can be formed using the digits 1 2 3 4 5 if digits Cannot be repeated?2 How many 3 digit numbers can be formed with the digits 1 2 3 4 and 5 which are divisible by 5 and in which the digits are not repeated?3 What is the value of a 3 digit number?4 How are three digit numbers formed in math?

Total Number of Numbers which can be formed by numbers 1,2,3,4,5 (without repeating digitsi) = 5*4*3*2*! = 5! = 120. Now, in half them unit’s digit will be bigger than the ten’s digit and in half of them it will be smaller.

How many 3 digit numbers can be formed with the digits 1 2 3 4 and 5 which are divisible by 5 and in which the digits are not repeated?

How many 3-digit numbers can be formed from the digits 1,2,3,4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed? Total possible numbers =5×4×3=60.

How many numbers are in a 4 digit number?

1 There are 4 numbers (any number from 0-9) in a 4-digit number and the starting number should be 1 or bigger than 1. 2 The thousands place in a 4-digit number cannot be 0. 3 The smallest 4 digit number is 1000 and the greatest 4 digit number is 9999. 4 There are 9000 four-digit numbers in all. More

What is the value of a 3 digit number?

The value, therefore, is 4 × 10 = 40. The third number 2 is the hundreds place. So 2 is multiplied by 100 and its value is 2 × 100 = 200. Therefore the number is 200 + 40 + 3 = 243. Decomposing a 3-digit number: In a three-digit number, there are three place values used – hundred’s, ten’s, and units.

How are three digit numbers formed in math?

In the same way, we can define three digit numbers as those which have digits in three place values – Units, Tens and Hundreds. These are also formed by combining any three single digit numbers. Look the simulation below to see how a 3-digit number is formed from the largest 2-digit number.

Which is the smallest 3 digit number in the world?

100 is the smallest 3-digit number and 999 is the greatest 3 digit number. A 3-digit number cannot start with 0; 10 tens make 1 hundred which is the smallest 3 digit number and 10 hundred make a thousand which is the smallest 4 digit number.

[embed]https://www.youtube.com/watch?v=s2-BVreD85Q[/embed]

Ex 7.1, 1 (i) - Chapter 7 Class 11 Permutations and Combinations (Term 2)

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Ex 7.1, 1 How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? 3 digit number : Number of 3 digit numbers with repetition = 5 × 5 × 5 = 125

How many 3

Problem 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated? Solution: Answer: 108. Let 3-digit number be XYZ.

How many 3

Solution : (i) When repetition of digits is allowed:
No. of ways of choosing firsy digits = 5
No. of ways of choosing second digit = 5
No. of ways of choosing third digit = 5
Therefore, total possible numbers `= 5 xx 5 xx 5 = 125`
(ii) When repetition of digits is not allowed:
No.

How many ways can a 3

So the number of 3-number combinations are- (1,2,3),(1,2,4),(1,3,4),(2,3,4). Each can be arranged in 6 ways, so we get 24 ways totally. So why is my answer different here?

How many 3 numbers can be formed from the digits 1 2 3 4 and assuming that I repetition of the digits is allowed II repetition of the digits is not allowed?

So, required number of ways in which three digit numbers can be formed from the given digits is 5×4×3=60. Tải thêm tài liệu liên quan đến nội dung bài viết How many 3 digit numbers can be formed using the digits 1 2 3 4 5 if digits can be repeated? How many 3

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Nếu sau khi đọc nội dung bài viết How many 3 digit numbers can be formed using the digits 1 2 3 4 5 if digits can be repeated? vẫn chưa hiểu thì hoàn toàn có thể lại Comments ở cuối bài để Ad lý giải và hướng dẫn lại nha #digit #numbers #formed #digits #digits #repeated - 2022-09-23 06:50:23