1) In an Engineering department at Stevens, there are 9 professors and 16 PhD st
ID: 3074533 • Letter: 1
Question
1) In an Engineering department at Stevens, there are 9 professors and 16 PhD students. The department decides to send 6 students and 4 professors to attend a conference in London. If Prof. X goes, exactly one of his 3 PhD students will go; if Prof. X does not go, none of his PhD students will go. The remaining professors and students have no such restrictions. a) In how many ways can the department select the group to attend the conference? b) If the selection is done at random, what is the probability that Prof. X will NOT go to the conference?Explanation / Answer
a) Department has to select 6 students and 4 professors to attend the conference.
We take two different cases:
Case 1: Prof. X attends the conference.
If Prof X attends the conference then we have to select 3 other professors from total 8 in 8C3 = 56 ways
Select exactly 1 of his 3 PhD students, and other 5 students from remaining 13 in: 3C1 x 13C5 = 3861 ways
Total ways to select the group = 56 x 3861 = 216216
Case 2: Prof X does not attends the conference
Select 4 professors from total 8 in 8C4 = 70 ways
Select 6 students from total 16 in 16C6 = 8008 ways
Total ways to select the group = 70 x 8008 = 560560
Total number of ways to select the group( Case 1 + Case 2) = 216216 + 560560 = 776776
b)
Total number of ways in which Prof X goes to the conference (from Case 1) = 216216
Total number of ways in which Prof X doesn't goes to the conference (from Case 2) = 560560
Total number of ways to select the group = 776776
Probability that Prof. X will NOT go to the conference = 560560/776776 = 0.722
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