How many numbers between 5000 and 10,000 can | vedclass

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

Question

(A) number between $5000$ and $10,000$ must be a $4$-digit number.The thousand's place can be filled by any of the digits $5, 6, 7, 8, 9$ to ensure th

Vedclass · Accepted Answer

$5 	imes ^{8}P_{3}$

Vedclass · Answer

(A) number between $5000$ and $10,000$ must be a $4$-digit number.The thousand's place can be filled by any of the digits $5, 6, 7, 8, 9$ to ensure the number is $\ge 5000$.Thus,the thousand's place can be filled in $5$ ways.Since each digit can appear at most once,we have $8$ remaining digits to fill the remaining $3$ places.The number of ways to arrange $3$ digits out of $8$ is given by the permutation formula $^{8}P_{3}$.Therefore,the total number of such numbers is $5 	imes ^{8}P_{3}$.

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if each digit appears not more than once in each number?

Similar Questions

How many $8$-digit numbers can be formed such that all digits are distinct?

The total number of permutations of the letters of the word "$BANANA$" is

Find the value of $n$ such that $^{n}P_{5} = 42 \, ^{n}P_{3}$,where $n > 4$.

In how many ways can $10$ true-false questions be replied?

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module