If the digits are not allowed to repeat in an | vedclass

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

Question

(D) We need to form numbers greater than $10,000$ using the digits $\{0, 2, 4, 6, 8\}$ without repetition. Since we have $5$ distinct digits,any numbe

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(D) We need to form numbers greater than $10,000$ using the digits $\{0, 2, 4, 6, 8\}$ without repetition. Since we have $5$ distinct digits,any number greater than $10,000$ must be a $5$-digit number.For a $5$-digit number,the first digit (ten-thousands place) cannot be $0$. Thus,the first digit can be chosen from $\{2, 4, 6, 8\}$,which gives $4$ choices.The remaining $4$ positions can be filled by the remaining $4$ digits in $P(4, 4) = 4 	imes 3 	imes 2 	imes 1 = 24$ ways.Therefore,the total number of such numbers is $4 	imes 24 = 96$.

If the digits are not allowed to repeat in any number formed by using the digits $0, 2, 4, 6, 8$,then the number of all numbers greater than $10,000$ is equal to $....$

Similar Questions

The number of ways of arranging all the letters of the word $PERFECTION$ such that there must be exactly two consonants between any two vowels is

If ${}^{27}P_{r+7} = 7722 \times {}^{25}P_{r+4}$,then $r = $

There are $5$ roads from a village to a city. In how many different ways can a villager go to the city and return back?

If the letters of the word $SACHIN$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $SACHIN$?

The sum of all the $4$-digit distinct numbers that can be formed with the digits $1, 2, 2,$ and $3$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module