930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student then what is the number of students in the class?

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Solution

$^{n} C_{2}$ groups. A gives card to B and B to A. Hence 2. $^{n} C_{2}$ = 930 or n(n-1) -930 = 0
or ( $n^{2}$ ) - n - 30 x 31 = 0
or (n-31) (n+30) = 0 $∴$ n=31

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930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student then what is the number of students in the class?

nC2 groups. A gives card to B and B to A. Hence 2. nC2 = 930 or n(n-1) -930 = 0or (n2) - n - 30 x 31 = 0or (n-31) (n+30) = 0 ∴ n=31

$^{n} C_{2}$ groups. A gives card to B and B to A. Hence 2. $^{n} C_{2}$ = 930 or n(n-1) -930 = 0
or ( $n^{2}$ ) - n - 30 x 31 = 0
or (n-31) (n+30) = 0 $∴$ n=31