The digits 4, 5, 6, 7, 8 are written in every | vedclass

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

Question

(C) Total number of $5$-digit numbers formed using the digits ${4, 5, 6, 7, 8}$ without repetition is $5! = 120$.To find the numbers greater than $560

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(C) Total number of $5$-digit numbers formed using the digits ${4, 5, 6, 7, 8}$ without repetition is $5! = 120$.To find the numbers greater than $56000$,we subtract the numbers less than or equal to $56000$ from the total.Numbers starting with $4$: There are $4! = 24$ such numbers.Numbers starting with $54$: There are $3! = 6$ such numbers.Numbers starting with $55$: Not possible as digits are distinct.Numbers starting with $56000$: Since the digits are ${4, 5, 6, 7, 8}$,the smallest number starting with $56$ is $56478$,which is already greater than $56000$.Thus,the numbers less than $56000$ are those starting with $4$ ($24$ numbers) and those starting with $54$ ($6$ numbers).Total numbers less than $56000 = 24 + 6 = 30$.Required numbers greater than $56000 = 120 - 30 = 90$.

The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

Similar Questions

How many different $2$-digit numbers can be formed using the digits $1, 2, 3, 4, 5, 6$,if no digit is repeated?

Out of $13$ cricket players,$4$ are bowlers. In how many ways can a cricket team of $11$ players be formed such that at least $2$ bowlers are included?

The number of ways in which an arrangement of $4$ letters of the word $PROPORTION$ can be made is

The number of arrangements of the letters of the word $CALCUTTA$ is:

In a group of $6$ boys and $4$ girls,four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

Vedclass Test Series

Exam Paper Generator

Online Exam Module