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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How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$

  • [AIEEE 2008]

There are $m$ books in black cover and $n$ books in blue cover, and all books are different. The number of ways these $(m+n)$ books can be arranged on a shelf so that all the books in black cover are put side by side is

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Find the number of words with or without meaning which can be made using all the letters of the word $AGAIN$. If these words are written as in a dictionary, what will be the $50^{\text {th }}$ word?