There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit

  • A

    $6720$

  • B

    $60480$

  • C

    $30$

  • D

    $346$

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  • [IIT 1968]

$^n{C_r} + {2^n}{C_{r - 1}}{ + ^n}{C_{r - 2}} = $

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