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) To form a $4$-digit number using the digits $1, 2, 3, 4, 5, 6, 7$ without repetition,we need to select $4$ digits out of $7$ and arrange them.
Th

Vedclass · Accepted Answer

$840$

Vedclass · Answer

(A) To form a $4$-digit number using the digits $1, 2, 3, 4, 5, 6, 7$ without repetition,we need to select $4$ digits out of $7$ and arrange them.
The number of ways to select and arrange $4$ digits out of $7$ is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.
Here,$n = 7$ and $r = 4$.
Number of ways = $^7P_4 = \frac{7!}{(7-4)!} = \frac{7!}{3!} = 7 	imes 6 	imes 5 	imes 4 = 840$.
Note: The original provided option $480$ is incorrect based on the standard permutation calculation for $4$ distinct digits from $7$.

How many $4$-digit numbers can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ such that each digit is used only once?

Similar Questions

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by $4$,when the repetition of any digit is not allowed,is:

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is

If $^n{P_r} = 720 \times {^n{C_r}}$,then $r$ is equal to:

How many $5$-digit numbers can be formed using the digits $3, 4, 7$ once each and the digit $5$ twice?

The number of ways in which the letters of the word $TRIANGLE$ can be arranged such that two vowels do not occur together is

Vedclass Test Series

Exam Paper Generator

Online Exam Module