CP #14

From GMATClub:

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?

(A) 144
(B) 131
(C) 115
(D) 90
(E) 45


OA: C
Chairmen shake hands 10*7=70 with business executives times. Business executives shake hands with each other 10 C 2 times or 45 times. The total is 115 .

Why 10C2?

10 business executives shakes hands with other 9 business executives in 10c2 ways = 45 ways
10c2 = 9+8+7+6+5+4+3+2+1 = 45

First executive shakes hands with remaining 9 executives
Second executive shakes hands with remaining 8 executives
Third executive shakes hands with remaining 7 executives
Fourth executive shakes hands with remaining 6 executives
Fifth executive shakes hands with remaining 5 executives
Sixth executive shakes hands with remaining 4 executives
Seventh executive shakes hands with remaining 3 executives
Eighth executive shakes hands with remaining 2 executives
Nineth executive shakes hands with remaining 1 executives
Tenth executive already shakes hands with all 9 executives.