Probability of winning in a competition (first, second and third)

[desmond iking]

Homework Statement

A and B are together with 5 other contestants take part in a competition. The winners are champion, first -runner up and second- runner up. Find the probability that A and B are winner

my working is 3/7 x 2/6= 1/7 the ans is correct.

but by doing so i assume A is selected first. then B is selected after this. why there's no another probability that i select B first , then i select A . which is also 3/7 x 2/6= 1/7.. so by adding 2 of the probability , i have 1/7 + 1/7 = 2/7

Homework Equations

The Attempt at a Solution

 

[cpscdave]

By doing the 3/7 x 2/6 you are counting both A being selected first as well as B being "selected" first
think about it
A 1st -> B 2nd or 3rd
A 2nd -> B 1st or 3rd
A 3rd -> B 1st or 2nd so those are A being selected first what if we did B first?

B 1st > A 2nd or 3rd but look both combinations here are counted already B1 A2 was counted in the 2nd row and B1 A3 was counted in the 3rd

hope that helps