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
$6720$
$60480$
$30$
$346$
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least one boy and one girl ?
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
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
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?