How many odd numbers of four digits can be fo | vedclass

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

Question

(A) four-digit number is odd if its unit place is occupied by an odd digit. The available odd digits from the set ${0, 1, 2, 3, 4, 7, 8}$ are ${1, 3,

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(A) four-digit number is odd if its unit place is occupied by an odd digit. The available odd digits from the set ${0, 1, 2, 3, 4, 7, 8}$ are ${1, 3, 7}$.$1$. The unit place can be filled by any of the $3$ odd digits in $^3P_1 = 3$ ways.$2$. The thousandth place cannot be $0$. Since one odd digit is already used in the unit place,there are $6 - 1 = 5$ remaining digits available for the thousandth place (excluding $0$ and the digit used in the unit place). Thus,it can be filled in $5$ ways.$3$. The remaining two places (hundredth and tenth) can be filled by the remaining $5$ digits in $^5P_2 = 5 	imes 4 = 20$ ways.Therefore,the total number of four-digit odd numbers is $3 	imes 5 	imes 20 = 300$.

How many odd numbers of four digits can be formed with the digits $0, 1, 2, 3, 4, 7$ and $8$?

Similar Questions

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is

In how many ways can $7$ men and $7$ women be seated around a round table such that no two women sit together?

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls,one in each box,could be placed such that a ball does not go to the box of its own colour is

There are $n$ white and $n$ black balls marked $1, 2, 3, ..., n$. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours are

Vedclass Test Series

Exam Paper Generator

Online Exam Module