Question

# involving the selection of officers in an advisory board. Assume that you have a total of...

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?

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

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