A school Science Fair team will consist of 2 male students, two female students and one alternate. The alternate can be of either sex. There are $4$ males (including Ted) and $5$ females (including Vanessa) trying out for the team. A team roster is a list of five students chosen without mention of which one of the five will be the alternate. If the five students are chosen randomly from among the nine trying out, find the probability that the team roster contains Ted and Vanessa.
I tried solving it by finding the situations where we pick 2 males out of 3 and 1 female out of 4 and 1 male out of 3 and 2 females out of 4 to find the possible outcomes and divided them with the total number of outcomes.
So i got $(3*4+3*6)/300$ which seems to be wrong as the answer is 3/10