Problem Solving

A certain club has 66 members, each of which is participating in
exactly one of the six projects in which the club is currently
involved. If the numbers of club members participating in the
projects are consecutive even numbers, what is the probability
that a given club member is participating in the project that the
fewest club members are participating in?


[spoiler]1/11[/spoiler]

please advice

We have 6 projects and 66 members.

Average member/ project = 66/6 = 11

first find the number of people in each project. Since they are even consecutive numbers, they will be arranged equally spaced around the mean

6 - 8 - 10- (11) - 12 - 14 - 16

So the project has 6-8-10-12-14-16 members respectively.

P(participating in fewest club member) = N(Fewest)/N(total) = 6/66 = 1/11

let the least number of people in a club = 2n
thus other clubs have - 2n+2, 2n+4 , ...2n+10 members each

adding all , 2n + 2n+2 + 2n+4 + ..+2n+10 = 66
gives n = 3

thus the number of members are 6,8,10,12,14,16

hence probability = 6/66 = 1/11