Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability intermediate

Problem

A club has members from each of different schools, for a total of members. How many possible ways are there to arrange a presidency meeting under the following conditions:

i. The club must choose one of the schools at which to host the meeting, and

ii. The host school sends representatives to the meeting, and each of the other two schools sends representative.
Solution
Pick one of the schools as the host. There are ways to select the two representatives from that school and ways to pick a representative from each of the other schools. So once we have selected a host school, there are ways to pick the representatives. However, any of the three schools can be the host, so we need to multiply by to get ways.
Final answer
750