If $2 \times {}^n{C_5} = 9\,\, \times \,\,{}^{n - 2}{C_5}$, then the value of $n$ will be
$7$
$10$
$9$
$5$
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
In a conference of $8$ persons, if each person shake hand with the other one only, then the total number of shake hands shall be
If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then
How many words, with or without meaning, each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?