There are 5 volumes of Mathematics among 25 b | vedclass

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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

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