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  • At the party hall, 10 families with a total of 3 people from each family exchanged new year greeting cards just once with each other. Find out how many card exchanges there are overall at

At the party hall, 10 families with a total of 3 people from each family exchanged new year greeting cards just once with each other. Find out how many card exchanges there are overall at the party.

Option: 1

410


Option: 2

810


Option: 3

730

 


Option: 4

405


Answers (1)

best_answer

There is 10 families total comprising 3 members in each family. 

The total number of persons in an event is given by,

10\times 3=30

Now every member of the family will exchange the card with 27 other persons. 

The total number of cards exchanged is given by,

27\times 30=810

As two persons exchange two cards with each other, the total number of card exchanges is half the number of cards.

So, the total number of card exchanges is,

\frac{810}{2}=405

Therefore, the number of ways in which the cards are exchanged is 405.

 

Posted by

Sanket Gandhi

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