The number of permutations of n things taken | vedclass

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(C) To find the number of permutations of $n$ things taken $r$ at a time,where $p$ specific things are always included:$1$. First,we select the remain

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$^{n-p}C_{r-p} 	imes r!$

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(C) To find the number of permutations of $n$ things taken $r$ at a time,where $p$ specific things are always included:$1$. First,we select the remaining $(r-p)$ items from the remaining $(n-p)$ items,which can be done in $^{n-p}C_{r-p}$ ways.$2$. Now,we have a total of $r$ items (the $p$ specific items plus the $r-p$ selected items).$3$. These $r$ items can be arranged among themselves in $r!$ ways.$4$. Therefore,the total number of permutations is $^{n-p}C_{r-p} 	imes r!$.

The number of permutations of $n$ things taken $r$ at a time,when $p$ specific things are always included,is

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