In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?
# of girls can be found out by 45 = G choose 2 which gives G = 10
# boys similarly can be found out by 105 = B choose 2 which gives B = 15
# of handshakes between boys and girts = 10 * 15 = 150