On the occasion of the Dipawali festival, eac | vedclass

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Question

(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 $B$

Vedclass · Accepted Answer

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

Vedclass · Answer

(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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