The number of integers greater than 6000 that | vedclass

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

Question

(B) To form an integer greater than $6000$,we can form $4$-digit or $5$-digit numbers.Case $1$: $4$-digit numbers greater than $6000$.The first digit

Vedclass · Accepted Answer

$840$

Vedclass · Answer

(B) To form an integer greater than $6000$,we can form $4$-digit or $5$-digit numbers.Case $1$: $4$-digit numbers greater than $6000$.The first digit can be $6, 7, 8,$ or $9$ ($4$ choices).The remaining $3$ positions can be filled by the remaining $5$ digits in $P(5, 3) = 5 	imes 4 	imes 3 = 60$ ways.Total $4$-digit numbers $= 4 	imes 60 = 240$.Case $2$: $5$-digit numbers.Since all $5$-digit numbers formed by these digits are greater than $6000$,we arrange $5$ distinct digits in $5$ positions.Total $5$-digit numbers $= 5! = 120$.Total integers $= 240 + 120 = 360$.Wait,re-evaluating the question: The digits are $0, 5, 6, 7, 8, 9$ (total $6$ digits).For $4$-digit numbers starting with $6, 7, 8, 9$:First digit: $4$ choices.Second digit: $5$ choices.Third digit: $4$ choices.Fourth digit: $3$ choices.Total $= 4 	imes 5 	imes 4 	imes 3 = 240$.For $5$-digit numbers:First digit cannot be $0$ ($5$ choices).Remaining $4$ positions: $P(5, 4) = 5 	imes 4 	imes 3 	imes 2 = 120$.Total $= 5 	imes 120 = 600$.Total $= 240 + 600 = 840$.

The number of integers greater than $6000$ that can be formed by using the digits $0, 5, 6, 7, 8,$ and $9$ without repetition is

Similar Questions

How many numbers can be formed using the digits $1, 2, 3, 4$ if repetition of digits is not allowed?

How many words can be formed using any $3$ letters from the word $UNIVERSAL$?

All the letters of the word $LETTER$ are arranged in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order. Then the rank of the word $TETLER$ is

If $n, r$ are two positive integers such that $1 \leq r < n$,then ${ }^{n} P_{r+1} + r^2 { }^{n-1} P_{r-1} + (r+1) { }^{n-1} P_{r} + r { }^{n-1} P_{r-1} =$

The number of all $5$-digit numbers with distinct digits is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module