There are 5 volumes of Mathematics among 25 b | vedclass

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

Question

(A) Total number of ways to arrange $25$ books is $25!$.Out of $25$ positions,we choose $5$ positions for the $5$ Mathematics volumes in ${}^{25}C_5$

Vedclass · Accepted Answer

$\frac{1}{5!}$

Vedclass · Answer

(A) Total number of ways to arrange $25$ books is $25!$.Out of $25$ positions,we choose $5$ positions for the $5$ Mathematics volumes in ${}^{25}C_5$ ways.Once these $5$ positions are chosen,there is only $1$ way to arrange the $5$ Mathematics volumes in increasing order.The remaining $20$ books can be arranged in the remaining $20$ positions in $20!$ ways.Therefore,the number of favourable arrangements is ${}^{25}C_5 	imes 1 	imes 20! = \frac{25!}{5! 	imes 20!} 	imes 20! = \frac{25!}{5!}$.The probability is $\frac{	ext{Favourable ways}}{	ext{Total ways}} = \frac{25! / 5!}{25!} = \frac{1}{5!}$.

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

Similar Questions

The number of ways of distributing $15$ apples to three persons $A, B, C$ such that $A$ and $C$ each get at least $2$ apples and $B$ gets at most $5$ apples is

There are three sections in a question paper,each section containing $4$ questions. If a candidate has to answer exactly $5$ questions from this paper such that at least one question is answered from each section,then the number of ways in which a candidate can make the choice of questions is

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of one man and one woman,is

In the prime factorization of $37! = 2^{\alpha_2} \cdot 3^{\alpha_3} \cdot 5^{\alpha_5} \cdots 37^{\alpha_{37}}$,the ratio $\alpha_3 : \alpha_5$ is:

The total number of positive integral solutions $(x, y, z)$ such that $xyz = 24$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module