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No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free 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 free classes today! Solution The correct option is C1380Explanation for the correct option:The total numbers can be formed.We have total 6 digits here which are 0,1,2,3,4,5 . (adsbygoogle = window.adsbygoogle || []).push({}); We have formed numbers that are greater than 3000we can write, 4-digit numbers, 5 digit numbers and 6 digit numbers.Thus, Four-digit numbers =3x5x4x3 =180Five-digit numbers =5x5x 4x3x2=600Six-digit numbers =5x5x4x3x2x1= 600Therefore the total numbers formed =180+600+600=1380Hence the correct option is C.Without considering different cases. 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 at the position representing the thousand position. That leaves us with six digits to choose from for this position and that can be made in $P(6,1) = \frac{6!}{(6-1)!} = \frac{6!}{5!}=6$, 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 $P(6,3) = \frac{6!}{(6-3)!} = \frac{6!}{3!}=6 \cdot5 \cdot4$, 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 $P(3,1)=\frac{3!}{(3-1)!}=\frac{3!}{2!}=3$, 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 $P(5,1)=\frac{5!}{(5-1)!}=\frac{5!}{4!}=5$, 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 $P(5,2)=\frac{5!}{(5-2)!}=\frac{5!}{3!}=5 \cdot4=20$, 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. Table of Contents
111 even numbers How many 4 digit Oddnumbers can be formed if no digit can be repeated?2240 How many numbers can be formed from 1 2 3 4 5 without repetition when the digit at the unit’s place must be greater than that in the ten’s place?Total Number of Numbers which can be formed by numbers 1,2,3,4,5 (without repeating digitsi) = 5*4*3*2*! = 5! = 120. How many 4 digit number greater than 4000 can be formed with repetition? While digit 4, 5, and 6 can take this place. Now, we have the remaining 4 numbers and the remaining three digits can be taken by any of them to form a number greater than 4000. Hence, the number of numbers that are greater than 4000 which can be formed using the digits 2, 3, 4, 5, 6 without repetition is 192. How many even numbers can be formed from the digits 12345? The number of 3 digit odd numbers, that can be formed by using the digits 1,2,3,4,5,6 when the repetition is allowed, is. How many 4 digit odd numbers can be formed from the digits 12345?The answer is 180 four-digit odd numbers. How do you make a number less than 4000?In order to be less than 4000 you can only use 1, 2, or 3 as the first digit — so there are 3 ways to choose the first digit. This leaves you with five digits to choose from for the second digit (you started with six digits to choose from and repetition is not allowed). What is the number with no repeated digit?Given a range find total such numbers in the given range such that they have no repeated digits. For example: 12 has no repeated digit. 22 has repeated digit. 102, 194 and 213 have no repeated digit. 212, 171 and 4004 have repeated digits. How do you write 2345 as a number? For example, 2345 is a 4-digit number. In the numeral form, it is written as 2,345. In words, it is written as: Two thousand three hundred forty-five. In the expanded form it is written as: 2000 + 300 + 40 + 5, or, 2 thousands + 3 hundreds + 4 tens + 5 ones. How many numbers are there in 3 5 4 3? For the third digit there are four digits to choose from (again, no repetitions), and for the fourth digit there are three digits to choose from. So overall there are 3 × 5 × 4 × 3 = 180 numbers. Thre are 3 choices for the first digit. For each of these, there are 5 choices for the second digit.
Post navigationHow many even numbers of 5 digits can be formed with the digits 1 2 3 4 and 5?∴ the total number of arrangements = 120 + 96 + 96 = 312. How many four digits numbers can be formed with the digit 1 2 3 4 which are greater than 3000 *?That means in total we have 72+120=192 numbers larger than 3,000. How many 3 digit even numbers can be made by using the digits 1 2 3 4 6 if repetition of digits is not allowed?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. How many 3 digit even numbers can be formed from the digits 0 1 2 3 4 and 5 when none of the digits are repeated?Count the number of 3-digit strings whose last digit is even. This gives 60−8=52 3-digit even numbers using digits from {0,1,2,3,4,5} without repetition. Show activity on this post. How many even three digit numbers can be formed?The number at one's place can be filled by 2, 4, 6. ∴ The required number of ways formed using 3- digit even number using 1, 2, 3, 4, 6, 7 is 60. How many 5Not a single five-digit prime number can be formed using the digits 1, 2, 3, 4, 5(without repetition). This is because if one adds the digits, the result obtained will be = 1 + 2 + 3 + 4 + 5 = 15 which is divisible by 3.
How many 5∴ the total number of arrangements = 120 + 96 + 96 = 312.
How many 51080. You can make 1080 5-digit even numbers from 1,2,3,4,5,6,7 if no digit is repeated. There are total 5 places. At unit place we can have 3 possibilities 2,4 & 6 to make number even.
How many 5Finally we can say that 120 five digit numbers can be formed using digits 1,2,3 with exactly one digit repeating 3 times. @Hackywacky Indeed I get 120 as well.
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