How many different numbers of three digits can be formed with the digits 1 2 3 4 5 no digit is being repeated? ✅ Vip
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Lê Minh Phương đang tìm kiếm từ khóa How many different numbers of three digits can be formed with the digits 1 2 3 4 5 no digit is being repeated? được Update vào lúc : 2022-09-20 11:50:19 . Với phương châm chia sẻ Kinh Nghiệm Hướng dẫn trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi Read Post vẫn ko hiểu thì hoàn toàn có thể lại Comment ở cuối bài để Tác giả lý giải và hướng dẫn lại nha.In mathematics, permutation is known as the process of arranging a set in which all the members of a set are arranged into some series or order. The process of permuting is known as the rearranging of its components if the set is already arranged. Permutations take place, in more or less important ways, in almost every area of mathematics. They frequently appear when different commands on certain finite sets are considered.
Nội dung chính- How many 3-digit even numbers can be formed by using the digits 1,2,3,4, and 5?Similar QuestionsHow many numbers of 3 digits can be formed with the digits 12345 repetition not allowed?How many number of 3 digits can be formed with the digits 12345?How many ways the three digits 1/2 and 3 can be arranged if repetition is allowed?How many 3 digit numbers can be formed without repeating?
What is a Combination?
A combination is an act of choosing items from a group, such that (not like permutation) the order of choice does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the union of n things taken k a time without repetition. In combination, you can select the items in any order. To those combinations in which re-occurrence is allowed, the terms k-selection or k-combination with replication are frequently used.
Permutation Formula
In permutation r things are selected from a set of n things without any replacement. In this order of selection matter.
nPr = (n!) / (n-r)!
Here,
n = set size, the total number of items in the set
r = subset size , the number of items to be selected from the set
Combination Formula
In combination r things are selected from a set of n things and where the order of selection does not matter.
nCr = n!/(n−r)!r!
Here,
n = Number of items in set
r = Number of items selected from the set
How many 3-digit even numbers can be formed by using the digits 1,2,3,4, and 5?
Solution:
If repetition is allowed
A three digit even number is to be formed from given 5 digits 1,2,3,4,5.
Ones place can be filled by 2 or 4 since the number is to be even. So, there are 2 ways to fill ones place.
Since, repetition is allowed , so tens place can be filled by 5 ways.
Likewise, hundreds place can also be filled by 5 ways.
So, number of ways in which three digit even numbers can be formed is 5 × 5 × 2 = 50
If repetition is not allowed
A three digit even number is to be formed from given 5 digits 1,2,3,4,5.
Ones place can be filled by 2 or 4 since the number is to be even. So, there are 2 ways to fill ones place.
Since, repetition is not allowed, so tens place can be filled by 4 ways.
Similarly, hundreds place can be filled by 3 ways.
So, number of ways in which three digit even numbers can be formed is 2 × 4 × 3 = 24
Similar Questions
Question 1: How many 3 digit odd numbers can be formed by using the digits 1,2,3,4 and 5?
Solution:
If repetition is allowed
A three digit odd number is to be formed from given 5 digits 1,2,3,4,5.
Ones place can be filled by 1, 3 or 5 since the number is to be odd. So,
there are 3 ways to fill ones place.
Since, repetition is allowed , so tens place can be filled by 5 ways.
Similarly, hundreds place can also be filled by 5 ways.
So, number of ways in which three digit odd numbers can be formed is 5×5×3=75
If repetition is not allowed
A three digit odd number is to be formed from given 5 digits 1,2,3,4,5.
Since, for the number is to be odd , so ones place can be filled by 1, 3 or 5. So,
there are 3 ways to fill ones place.
Since, repetition is not allowed , so tens place can be filled by 4 ways.
Similarly, hundreds place can be filled by 3 ways.
So, number of ways in which three digit odd numbers can be formed is 3×4×3 =36
Question 2: How many 4 digit even numbers can be formed by using the digits 1,2,3,4 and 5?
Solution:
If repetition is allowed
A four digit even number is to be formed from given 5 digits 1,2,3,4,5.
Since, for the number is to be even, so ones place can be filled by 2 or 4. So, there
are 2 ways to fill ones place.
Since, repetition is allowed, so tens place can be filled by 5 ways.
Similarly, hundreds place can also be filled by 5 ways.
Similarly, thousandth place can also be filled by 5 ways
So, number of ways in which four digit even numbers can be formed is 5 × 5 × 5 × 2 = 250
If repetition is not allowed
A four digit even number is to be formed from given 5 digits 1,2,3,4,5.
Since, for the number is to be even, so ones place can be filled by 2 or 4. So,
there are 2 ways to fill ones place.
Since, repetition is not allowed, so tens place can be filled by 4 ways.
Similarly, hundreds place can be filled by 3 ways.
Similarly, thousandth place can be filled by 2 ways
So, number of ways in which four digit even numbers can be formed is 2 × 4 × 3 × 2 = 48
How many numbers of 3 digits can be formed with the digits 12345 repetition not allowed?
Answer: 60. Let 3-digit number be XYZ.How many number of 3 digits can be formed with the digits 12345?
∴ Total number of 3-digit numbers = 3×4×5=60.How many ways the three digits 1/2 and 3 can be arranged if repetition is allowed?
Answer: 125 As repetition is allowed, So the number of digits available for B and C will also be 5 (each).How many 3 digit numbers can be formed without repeating?
n will be the number of digits that are not in 0, 2, 3, 4, 5 and 6. Hence 1, 7, 8, 9. The value of r will be 3, as we need a form 3 digit number only. Hence, 24 3-digits numbers can be formed without using the digits 0, 2, 3, 4, 5 and 6. Tải thêm tài liệu liên quan đến nội dung bài viết How many different numbers of three digits can be formed with the digits 1 2 3 4 5 no digit is being repeated?