How many numbers can be formed with the digit | vedclass

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

Question

(C) The given digits are $1, 2, 3, 4, 3, 2, 1$. There are $7$ digits in total.Out of these,the odd digits are $1, 3, 3, 1$ (total $4$ digits) and the

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(C) The given digits are $1, 2, 3, 4, 3, 2, 1$. There are $7$ digits in total.Out of these,the odd digits are $1, 3, 3, 1$ (total $4$ digits) and the even digits are $2, 4, 2$ (total $3$ digits).The odd places are $1^{st}, 3^{rd}, 5^{th},$ and $7^{th}$ (total $4$ places).The even places are $2^{nd}, 4^{th},$ and $6^{th}$ (total $3$ places).Since odd digits must occupy the odd places,the $4$ odd digits $(1, 1, 3, 3)$ can be arranged in $4$ odd places in $\frac{4!}{2!2!} = \frac{24}{4} = 6$ ways.The $3$ even digits $(2, 2, 4)$ can be arranged in $3$ even places in $\frac{3!}{2!1!} = \frac{6}{2} = 3$ ways.Therefore,the total number of ways to form the numbers is $6 	imes 3 = 18$.

How many numbers can be formed with the digits $1, 2, 3, 4, 3, 2, 1$ so that odd digits always occupy the odd places?

Similar Questions

$^{80}C_{40}$ is not divisible by -

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

Out of $10$ points in a plane,$6$ are in a straight line. The number of triangles formed by joining these points is:

In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?

If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^nC_{r-1} + ^nC_r = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module