10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
Can someone explain to me why its 10 C 2?
This question deals with the concept of "Combination". The difference between Permutation and Combination is that in Combination "order" does not matter. Say, if A is shaking hands with B, it's equivalent to B shaking hands with A and either of the event shall be counted as One only. Similarly, in case of A, B & C, the no of "orders" possible is 3 C 2 = 3 ( A & B, B & C and A & C). So this type of counting is done using formula nCr, where n is total no of participants and r is no. of participants in one activity.
Accordingly, when there are 10 people, while 2 shake hands at a time, total no of possible is 10 C 2.