Thủ Thuật Hướng dẫn How many different 3 digits numbers can be formed using the digital 1 2 3 5 6 and 8 2022
Hà Trần Thảo Minh đang tìm kiếm từ khóa How many different 3 digits numbers can be formed using the digital 1 2 3 5 6 and 8 được Update vào lúc : 2022-11-21 00:26:03 . Với phương châm chia sẻ Thủ Thuật Hướng dẫn trong nội dung bài viết một cách Chi Tiết Mới Nhất. Nếu sau khi tham khảo Post vẫn ko hiểu thì hoàn toàn có thể lại phản hồi ở cuối bài để Mình lý giải và hướng dẫn lại nha.Complete step-by-step solution:
In this question, we are asked how many 3 digit numbers can be formed using the digits 0, 1, 3, 5, 7 where repetition is allowed.
Given digits: 0, 1, 3, 5, 7
Therefore, there are a total of 5 digits.
Now, as we have to form 3 digit numbers, let us draw three boxes.
- How many 3-digit even numbers can be formed by using the digits 1,2,3,4, and 5?Similar QuestionsHow many 3 digit numbers can be formed without using digits 1 2 3 9 5 repetition of digits are not allowed?How many different 3 digit numbers can be formed from the digital?How many 3 digit numbers can be formed using all the 3 digits 1/2 and 3?How many 3 digit numbers can be formed with the digits 1 2 3 4 5 repetition of digits not allowed?
First box will be hundreds, the second box will be tens and the third box will be ones.
Now, as the number is 3 – digit, the first box cannot use digit 0, because if we use 0 as first digit, the number will not be a 3 digit number. So, only 4 digits that are 1, 3, 5 and 7 can be used in the first box.
Therefore, there are 4 ways to fill the first box.
Now, for the second box, any out of the 5 given digits can be used to fill the box as repetition is allowed.
Therefore,
And for the third box too, we can fill it using any of the 5 given digits. Therefore, we get
So, therefore the total ways for forming 3 digit number will be
$ Rightarrow $Total ways of arrangement $ = 4 times 5 times 5 = 100$
Therefore, a
total of $100$ 3 digit numbers can be formed using the digits 0, 1, 3, 5, 7 when repetition is allowed.
Note: Here, note that if repetition were not allowed, then we would have got different answers.
For first digit:
As we have to form a 3 digit number, we cannot use 0 as the first digit. So,
For second digit:
Now, suppose we used 1 as the first digit, so now it cannot be used again for the second and third digit. So, the second digit can be 0, 3, 5 or 7. Therefore,
For third digit:
Suppose we used 3 as the second digit, so now 3 cannot be used for the third digit. So, the third digit can be 0, 5 or 7. Therefore,
$ Rightarrow $Total numbers formed when repetition is not allowed$ = 4 times 4 times 3 = 48$
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.
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 3 digit numbers can be formed without using digits 1 2 3 9 5 repetition of digits are not allowed?
Hence, the required number of numbers = 4 + 12 + 24 + 24= 64.How many different 3 digit numbers can be formed from the digital?
If you do allow repetition then you have five choices for each of the three places in the 3-digit number. 5^3 is 125. If you do not allow repetition then you have five choices for the first digit, four for the second, and three for the third. Here the answer is 5 x 4 x 3, or 60.How many 3 digit numbers can be formed using all the 3 digits 1/2 and 3?
The answer is 4!/(4-2)! = 12.How many 3 digit numbers can be formed with the digits 1 2 3 4 5 repetition of digits not allowed?
∴ Total number of 3-digit numbers = 3×4×5=60. Q.. Tải thêm tài liệu liên quan đến nội dung bài viết How many different 3 digits numbers can be formed using the digital 1 2 3 5 6 and 8