A school Science Fair team will consist of two male students, two female student

Question

A school Science Fair team will consist of two male students, two female students, and one "alternate". The alternate can be of either sex. There are four males (including Ted) and five females (including Vanessa) trying out for the team. A Team Roster is a list of the 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 both Ted and Vanessa. 8/25 2/25 2/9 3/10 none of the above I'

Explanation / Answer

case 1= ted is alternate so favourable ways 3C2*5C2 = 3*10 =30

case 2= venessa is alternate so favourable ways = 4C2*4C2 = 36

case 2= ted and venessa are not alternate so favourable ways = 3C1*4C1*5C1 = 60

total favourable ways = 30+36+60 = 126

total no. of ways = 4C2*5C2*5C1 = 6*10*5 = 300

probability = 126/300

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