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
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
- A
$^{20}{C_2}$
- B
$2\;.{\;^{20}}{C_2}$
- C
$2\;.{\;^{20}}{P_2}$
- D
None of these
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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
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The number of ways of dividing $52$ cards amongst four players equally, are
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- [IIT 1979]
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
The students $S _{1}, S _{2}, \ldots \ldots, S _{10}$ are to be divided into $3$ groups $A , B$ and $C$ such that each group has at least one student and the group $C$ has at most $3$ students. Then the total number of possibilities of forming such groups is ........ .
The students $S _{1}, S _{2}, \ldots \ldots, S _{10}$ are to be divided into $3$ groups $A , B$ and $C$ such that each group has at least one student and the group $C$ has at most $3$ students. Then the total number of possibilities of forming such groups is ........ .
- [JEE MAIN 2021]
$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 - r}{C_3} = $
$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 - r}{C_3} = $
- [IIT 1980]