Mẹo về How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated? Chi Tiết
Bạn đang tìm kiếm từ khóa How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated? được Cập Nhật vào lúc : 2022-09-19 14:40:24 . Với phương châm chia sẻ Bí kíp Hướng dẫn trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi tìm hiểu thêm nội dung bài viết vẫn ko hiểu thì hoàn toàn có thể lại Comments ở cuối bài để Ad lý giải và hướng dẫn lại nha.
Without considering different cases.
Nội dung chính
- The correct option is B
18
Explanation for the correct option:Finding the number of possibility.The digits are 0,1,2,3There are four positions in which digits can be arranged.In first position, zero cannot be placed. Since four digit number cannot be formed with zero.
So, we can form digits with 1,2,3. Thus there are 3 possibilities.In second position, we can place any of the remaining three digits. So it has 3 possibilities.In third position, we can
place the remaining two digits. So it has 2 possibilities.In fourth position, we can place either 0or2, because the number should be an even number. So, it has only 1
possibility.Thus, to form an even four digit number, the number of possibilities is=3×3×2×1=18Hence, option (B) 18 is the correct
answer. - How many 4 digit numbers can be formed by using the digits 1.2 5.6 7.8 Repetition is allowed )?
- How many 4 digit codes can be formed from the digits 1 3 5 7 and 9 if repetition of digits is not allowed?
- How many 4 digit numbers can be made using 0 7 with none of the digits being repeated?
- How many 4 digit numbers can you make without repeating digits?
This is another way to get the same answer as already answerd above.
Here we start by finding the total amount of the four-digit numbers with distinct digits, then finding the amount of odd digits, filling the same criteria, and last, we subtract the odd numbers from the total, to find the even numbers filling the criteria.
We have totally seven digits. We know that the digit zero cannot be placed the position
representing the thousand position. That leaves us with six digits to choose from for this position and that can be made in
$P(6,1) = frac6!(6-1)! = frac6!5!=6$, different ways.
Now, we have three positions left to fill and six digits to choose from, including the digit zero, which can be placed anywhere in the remaining positions. This choice can be done in
$P(6,3) = frac6!(6-3)! = frac6!3!=6 cdot5 cdot4$, different ways.
Finally,
with distinct digits, there is
$6 cdot6 cdot5 cdot4 =720$
four-digit numbers to be constructed.
We know that the amount of odd numbers plus the amount of even numbers equal the total amount of the 720 four-digit numbers.
The odd numbers are 1, 3 and 5. The question to be asked is how many of the 720 are odd?
The digit to fill the unit position can only be chosen from the digits 1, 3 or 5, and this choice can be made in
$P(3,1)=frac3!(3-1)!=frac3!2!=3$,
different ways.
To choose the digit filling the thousand position, we have five valid digits to choose from, since the zero digit is not valid for this position. The choice can be made in
$P(5,1)=frac5!(5-1)!=frac5!4!=5$, different ways.
Now we are left with two positions to fill, the hundred and tenth position, and five digits to choose from, now including the zero digit. The choice for these two positions can be made in
$P(5,2)=frac5!(5-2)!=frac5!3!=5
cdot4=20$, different ways.
The total number of odd four-digit numbers, with distinct digits are
$5 cdot5 cdot4 cdot3 =300$.
Now, we can answer the question how many of these 720, four-digit numbers, are even, by the subtraction
$720-300=420$.
The even numbers are 420.
No worries! We‘ve got your back. Try BYJU‘S không lấy phí classes today!
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
No worries! We‘ve got your back. Try BYJU‘S không lấy phí classes today!
No worries! We‘ve got your back. Try BYJU‘S không lấy phí classes today!
Solution
The correct option is B
18
Explanation for the correct option:Finding the number of possibility.The digits are 0,1,2,3There are four positions in which digits can be arranged.In first position, zero cannot be placed. Since four digit number cannot be formed with zero.
So, we can form digits with 1,2,3. Thus there are 3 possibilities.In second position, we can place any of the remaining three digits. So it has 3 possibilities.In third position, we can
place the remaining two digits. So it has 2 possibilities.In fourth position, we can place either 0or2, because the number should be an even number. So, it has only 1
possibility.Thus, to form an even four digit number, the number of possibilities is=3×3×2×1=18Hence, option (B) 18 is the correct
answer.
Concept:
Suppose there are k places to fil and n numbers, so first place can be filled by n ways, second place can be filled by (n-1) and last place can be filled by n+1 – k ways
Now total number of ways = n× (n – 1) × ……× (n + 1 – k)
Calculation:
For even no, last digit must be 0, 2, 4, 6
I: In first place 6 numbers can be filled, second 5 numbers, third 4 numbers, fourth and
last place always contain 0 i.e., only one number
So, total number of such numbers = 6 × 5 × 4 = 120
But we need four-digit number so first digit cannot be 0
II: In first place 5 numbers can be filled, second 5 numbers (zero will be there), third 4 numbers, fourth and last place always contain 2, i.e., only one number
So, total number of such numbers = 5 × 5 × 4 = 100
III: In first place 5 numbers can be filled, second 5 numbers (zero will be there), third 4
numbers, fourth and last place always contain 4, i.e., only one number
So, total number of such numbers = 5 × 5 × 4 = 100
IV: In first place 5 numbers can be filled, second 5 numbers (zero will be there), third 4 numbers, fourth and last place always contain 6, i.e., only one number
So, total number of such numbers = 5 × 5 × 4 = 100
Now,
Total number of 4 digits even numbers
= 120 + 100 + 100 + 100
= 420
Hence, option (1) is
correct.
With hundreds of Questions based on Permutations and Combinations, we help you gain expertise on Mathematics. All for không lấy phí. Explore Testbook Learn to attain the subject expertise with us.
How many 4 digit numbers can be formed by using the digits 1.2 5.6 7.8 Repetition is allowed )?
∴ 1296 four-digit numbers can be formed if repetition of digits is allowed.
How many 4 digit codes can be formed from the digits 1 3 5 7 and 9 if repetition of digits is not allowed?
<br> Number of 4-digit numbers `=(4xx3xx2xx1)=24. ` <br> Hence, the number of required numbers `=(4+12+24+24)=64. ` Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
How many 4 digit numbers can be made using 0 7 with none of the digits being repeated?
Hence, there are 4⋅7⋅6⋅5=840 possible numbers in this case.
How many 4 digit numbers can you make without repeating digits?
So there are 210 different combinations of four digits chosen from 0-9 where the digits don’t repeat.
Tải thêm tài liệu liên quan đến nội dung bài viết How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated?
Reply
6
0
Chia sẻ
Chia Sẻ Link Cập nhật How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated? miễn phí
Bạn vừa Read tài liệu Với Một số hướng dẫn một cách rõ ràng hơn về Clip How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated? tiên tiến và phát triển nhất và Chia SẻLink Download How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated? miễn phí.
Thảo Luận vướng mắc về How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated?
Nếu sau khi đọc nội dung bài viết How many 4 digit numbers can be made using 1.2 3.4 5.6 and 7 with none of the Digts being repeated? vẫn chưa hiểu thì hoàn toàn có thể lại phản hồi ở cuối bài để Tác giả lý giải và hướng dẫn lại nha
#digit #numbers #Digts #repeated