On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is
$^{20}{C_2}$
$2\;.{\;^{20}}{C_2}$
$2\;.{\;^{20}}{P_2}$
None of these
$\sum\limits_{r = 0}^m {^{n + r}{C_n} = } $
Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is
The total number of different combinations of one or more letters which can be made from the letters of the word ‘$MISSISSIPPI$’ is
A group of $9$ students, $s 1, s 2, \ldots, s 9$, is to be divided to form three teams $X, Y$ and, $Z$ of sizes $2,3$ , and $4$, respectively. Suppose that $s_1$ cannot be selected for the team $X$, and $s_2$ cannot be selected for the team $Y$. Then the number of ways to form such teams, is. . . .
Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -