(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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(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 $^{n-p}C_{r-p} \times r!$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Easy

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

A
$^nC_r \times p!$
B
$^{n-p}C_r \times r!$
C
$^{n-p}C_{r-p} \times r!$
D
None of these

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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

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