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

The total number of numbers greater than $100$ and divisible by $5$,that can be formed from the digits $3, 4, 5, 6$,if no digit is repeated is:

In how many ways can the letters of the word '$NUTAN$' be arranged when consonants occupy odd places and vowels come on even places?

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is

In how many ways can a committee,consisting of $5$ men and $6$ women,be formed from $8$ men and $10$ women?

If $11$ members of a committee sit at a round table so that the President and Secretary always sit together,then the number of arrangements is

Vedclass Test Series

Exam Paper Generator

Online Exam Module