question archive While selecting a 7 member student council committee, all students in grades 9-12 are equally likely to be selected
While selecting a 7 member student council committee, all students in grades 9-12 are equally likely to be selected
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While selecting a 7 member student council committee, all students in grades 9-12 are
equally likely to be selected. If there are 5 grade 9s, 11 grade 10s, 7 grade 11s and 15 grade
12s interested in being part of the committee, what is the probability that the student council
will have at least 2 grade 12 students?
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P12 = 5
2,103,376
Step-by-step explanation
There are:
Grade 9 - 5 students
Grade 10 - 11 students
Grade 11 - 7 students
Grade 12 - 15 students
Total - 38 students
All students from grades 9-12 have equal chances to be selected. Hence, all 38 students regardless of what grade they belong can be chosen as a member of the student council committee.
The number of ways to select the 7-member committee is given by:
nCr = n!
r! (n - r)!
Given:
n = 38
r = 7
Solution:
nCr = n!
r! (n - r)!
38C7 = 38!
7! (38 - 7)!
38C7 = 12620256
Hence, there are 12,620,256 ways to form a 7-member committee. If there are 15 grade 12 students, then the probability of selecting a grade 12 student is:
P12 = 15/12,620,256
or
P12 = 5/4,206,752
If two grade 12 students were to be selected, then the probability is:
P12 = (5/4,206,752) x 2
P12 = 5/2,103,376
