In a sports quiz , each participant is required to answer a question , 2 of which are on badminton and 3 on soccer . THe questions are kept in separate envelopes . These envelopes are numbered 1 to 5 . The four participants are A,B C and D . They are required to pick their own questions randomly .

For each participants , what is the probability that he will be the first to pick a question on badminton.

so this is what i have in mind , its either he picks badminton (B) first , then 2nd guy pick B , then the rest soccers (BBSS) , or (BSBS) or (BSSS)

there are 3 cases here , (2/5)(3/5)(3/5)(3/5)+(2/5)(3/5)(2/5)(3/5)+(2/5)(3/5)(3/5)(3/5) but the answer given is 3/10 . Erm , i cant see my mistake here .