Question

involving the selection of officers in an advisory board. Assume that you have a total of 15 people on the board: 3 out-of-state seniors, 5 in-state seniors, 2 out-of-state non-seniors, and 5 in-state non-seniors. University rules require that at least one in-state student and at least one senior hold one of the three offices. Note that if individuals change offices, then a different selection exists.

In how many ways can the officers be chosen while still conforming to University rules?

Answer 1

solution

we have the following officers

out of state in state total

senior 3 5 8

student 2 5 7

total 5 10 15

we have to form a advisory board of thee members in which according to the rule

1) atleast one instate student 2) atleast one senior hold one of the three offices

total number of ways 3 members can be selected out of 15 are ways

case1) selecting one instate student and 2 seniors

case2) selecting two instate student and 1 senior

case3) selecting one instate student and one senior and one from the other

so the required probability = probability of case1 +probability of case2 + probability of case3

for case 1) =

for case 2)

for case 3)  

case1+case2+case3 = (5*28)+(10*8) + (5*8*2) = 300 ways