How many numbers lying between 999 and 10000 | vedclass

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

Question

(C) The numbers lying between $999$ and $10000$ are all $4$-digit numbers.The total number of $4$-digit numbers that can be formed using the digits ${

Vedclass · Accepted Answer

$300$

Vedclass · Answer

(C) The numbers lying between $999$ and $10000$ are all $4$-digit numbers.The total number of $4$-digit numbers that can be formed using the digits ${0, 2, 3, 6, 7, 8}$ without repetition is given by $^6P_4 = \frac{6!}{(6-4)!} = 6 	imes 5 	imes 4 	imes 3 = 360$.However,a $4$-digit number cannot begin with the digit $0$. We must exclude those cases where $0$ is in the thousands place.If the thousands place is fixed as $0$,the remaining $3$ places can be filled by the remaining $5$ digits ${2, 3, 6, 7, 8}$ in $^5P_3 = \frac{5!}{(5-3)!} = 5 	imes 4 	imes 3 = 60$ ways.Therefore,the required number of $4$-digit numbers is $360 - 60 = 300$.

How many numbers lying between $999$ and $10000$ can be formed with the help of the digits $0, 2, 3, 6, 7, 8$ when the digits are not to be repeated?

Similar Questions

If ${}^n P_r = {}^{(n-1)} P_r + x \cdot {}^{(n-1)} P_{(r-1)}$,$\forall n, r \in N$ and $r \leq n$,then $x =$

$n$-digit numbers are formed using only three digits $2, 5,$ and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed is:

The number of ways in which the following prizes can be given to a class of $20$ boys,first and second Mathematics,first and second Physics,first Chemistry,and first English is:

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 $1$?

How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

Vedclass Test Series

Exam Paper Generator

Online Exam Module