The sum of all the 4-digit numbers formed by | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To find the sum of all $4$-digit numbers formed using the digits ${0, 3, 6, 9}$ without repetition,we first note that the total number of such $4$

Vedclass · Accepted Answer

$115992$

Vedclass · Answer

(B) To find the sum of all $4$-digit numbers formed using the digits ${0, 3, 6, 9}$ without repetition,we first note that the total number of such $4$-digit numbers is $3 	imes 3 	imes 2 	imes 1 = 18$.Step $1$: Calculate the sum of all $4$-digit numbers formed by ${0, 3, 6, 9}$ (including those starting with $0$).The sum of digits is $0+3+6+9 = 18$. Each digit appears in each place $3! = 6$ times.The sum of digits at each place is $6 	imes 18 = 108$.The total sum is $108 	imes (1000 + 100 + 10 + 1) = 108 	imes 1111 = 119988$.Step $2$: Calculate the sum of all $3$-digit numbers formed by ${3, 6, 9}$ (these are the numbers starting with $0$ in the $4$-digit set).The sum of digits is $3+6+9 = 18$. Each digit appears in each place $2! = 2$ times.The sum of digits at each place is $2 	imes 18 = 36$.The sum of these numbers is $36 	imes (100 + 10 + 1) = 36 	imes 111 = 3996$.Step $3$: Subtract the sum of numbers starting with $0$ from the total sum.Sum $= 119988 - 3996 = 115992$.

The sum of all the $4$-digit numbers formed by taking all the digits from ${0, 3, 6, 9}$ without repetition is

Similar Questions

If a seven-digit number formed with distinct digits $4, 6, 9, 5, 3, x,$ and $y$ is divisible by $3$,then the number of such ordered pairs $(x, y)$ is

If $x={ }^{16} C_5+{ }^{12} C_4, y=\sum_{r=1}^3{ }^{(20-r)} C_4, z=\sum_{k=1}^4{ }^{(16-k)} C_3$,then $x+y+z=$

In how many ways can $5$ distinct balls be distributed among $3$ persons such that each person receives at least one ball?

The number of seven-digit numbers that can be formed by using the digits $1, 2, 3, 5,$ and $7$ such that each digit is used at least once is:

The number of numbers between $2000$ and $5000$ that can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits not allowed) and are multiples of $3$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module