anthony and michael hot for eachother :wink: (counting)

[ashish1354]

i count the number of committees including Michel as following

let the committees be structured as : A B C
Order is not important
so, Michael comes in place of A
Place B can be taken by any of the 5 people left
Place C can be taken by any of the 4 people left

so possible committees including Michael = 1 x 5 x 4=20

but alternatively,

A is taken by Michael so 1 way
rest of the two places can be taken in 5c2 ways
so number of committees including Michael = 1 x 5c2=10

i need to know which solution is right and why is it so?

[anitaPEZ]

I know it's not the most clever way but lets say there are six members - member 1 is Michael, member 2 is Anthony, member 3, 4, 5 and 6.

So the possible committees in which Michael is a member are:

123
124
125
126
134
135
136
145
146
156

There are 10. Out of them, only 4 include Anthony. So the answer is 40%.