On the occasion of the Dipawali festival,each | vedclass

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(B) Each student sends a card to every other student. This means for every pair of students $(A, B)$,student $A$ sends a card to $B$ and student $B$ s

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${}^{20}P_{2}$

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(B) Each student sends a card to every other student. This means for every pair of students $(A, B)$,student $A$ sends a card to $B$ and student $B$ sends a card to $A$. This is a permutation problem where we need to arrange $2$ students out of $20$ in a specific order (sender and receiver). The number of ways to arrange $2$ students out of $20$ is given by the permutation formula ${}^{n}P_{r} = \frac{n!}{(n-r)!}$. Here $n = 20$ and $r = 2$,so the number of cards is ${}^{20}P_{2} = 20 	imes 19 = 380$. Alternatively,this is equal to ${}^{20}C_{2} 	imes 2! = \frac{20 	imes 19}{2 	imes 1} 	imes 2 = 380$.

On the occasion of the Dipawali festival,each student of a class sends a greeting card to every other student. If there are $20$ students in the class,the total number of greeting cards sent by the students is:

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