How many different nine-digit numbers can be | vedclass

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

Question

(C) The given number is $223355888$. The digits are $2, 2, 3, 3, 5, 5, 8, 8, 8$.Total digits = $9$. The positions are $1, 2, 3, 4, 5, 6, 7, 8, 9$.Even

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) The given number is $223355888$. The digits are $2, 2, 3, 3, 5, 5, 8, 8, 8$.Total digits = $9$. The positions are $1, 2, 3, 4, 5, 6, 7, 8, 9$.Even places are $2, 4, 6, 8$ (total $4$ places).Odd digits are $3, 3, 5, 5$ (total $4$ digits).Even digits are $2, 2, 8, 8, 8$ (total $5$ digits).Step $1$: Arrange the $4$ odd digits in the $4$ even places. The number of ways is $\frac{4!}{2! 	imes 2!} = \frac{24}{4} = 6$.Step $2$: Arrange the $5$ even digits in the remaining $5$ odd places. The number of ways is $\frac{5!}{2! 	imes 3!} = \frac{120}{2 	imes 6} = 10$.Total number of ways = $6 	imes 10 = 60$.

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits so that the odd digits occupy even places?

Similar Questions

How many $3$-digit numbers are there with no digit repeated?

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

How many words can be formed out of the letters of the word '$EDUCATION$' such that vowels occupy the odd positions?

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module