step by step please A group of people in a room each exchang

step by step, please.

A group of people in a room each exchange business cards. How many cards are exchanged when there are four people in the room? How many more cards are exchanged if one more person cones into the room? Relate the number of cards exchanged to the number of handshakes if the custom is to always shake hands before exchanging cards.

Solution

Dear Student Thank you for using Chegg !! Given total number of people in the room (N) = 4 No for exchanging cards we have two select 2 individuals from given N people No of ways of selected of 2 people from N = NC2 Since here no of people is 4 the above number becomes = 4C2 = 6 Now both the selected individuals shall give each other cards Hence cards exchanged between selected individuals = 2 nos Total number of cards exchanged = 6*2 = 12 nos Now if 1 more person enters the room N = 5 Total number of cards exchanged is given by = NC2 * 2 = 5C2 * 2 = 20 nos Now had it been a handshake problem, in that case no of handshakes between 2 selected individuals had been 1 So the general formula would have been = NC2 * 1 Hence Total no cards exchanged = 2 * Number of handshakes