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
Get Answers For Free
Most questions answered within 1 hours.