How many 4-digit numbers can be formed using | vedclass

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

Question

(A) Total $4$-digit numbers that can be formed using the digits ${0, 1, 2, 3, 4, 5, 6, 7}$ (where the first digit cannot be $0$) is $7 	imes 8 	imes

Vedclass · Accepted Answer

$1522$

Vedclass · Answer

(A) Total $4$-digit numbers that can be formed using the digits ${0, 1, 2, 3, 4, 5, 6, 7}$ (where the first digit cannot be $0$) is $7 	imes 8 	imes 8 	imes 8 = 3584$.Total $4$-digit numbers that can be formed without using the digit $1$ (using digits ${0, 2, 3, 4, 5, 6, 7}$) is $6 	imes 7 	imes 7 	imes 7 = 2058$.The number of $4$-digit numbers containing at least one $1$ is the total number of $4$-digit numbers minus the number of $4$-digit numbers without any $1$.Required numbers $= 3584 - 2058 = 1526$.Note: The provided option $D$ $(750)$ is incorrect based on the standard interpretation of this combinatorial problem. The correct calculation yields $1526$.

How many $4$-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that at least one digit is $1$?

Similar Questions

If all the letters of the word $MASTER$ are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order,then the rank of the word $MASTER$ is

The number of natural numbers less than $7,000$ which can be formed by using the digits $0, 1, 3, 7, 9$ (repetition of digits allowed) is equal to

$A$ car will hold $2$ persons in the front seat and $1$ person in the rear seat. If among $6$ persons $2$ can drive,then the number of ways in which the car can be filled is

In how many ways can the letters of the word $GARDEN$ be arranged such that the vowels appear in alphabetical order?

The number of different permutations that can be formed by taking $4$ letters at a time from the letters of the word '$REPETITION$' is

Vedclass Test Series

Exam Paper Generator

Online Exam Module