Question

Students are in a class. 16 are civil engineering (CE) majors, 7 are computer science majors (CS), 10 are business majors (B), 6 are math majors (M), 2 are English majors (E), and 4 are animal science majors (AS). If you randomly select 8 students from the class without replacement and without regard to order, give the number of ways the following events could occur.

a) Exactly 4 of the students are CS majors

b) 2 E, 3 CE, 1 AS, 1 M, 1 CS

Answer 1

a) Exactly 4 of the students are CS majors - 2583525

b) 2 E, 3 CE, 1 AS, 1 M, 1 CS - 94080

Explanation:

1) In total 8 students need to be selected out of total 45 students

4 need to be selected from CS stream and the other 4 will be selected from the remaining 38 student.

Probability of selecting 4 CS students =
`^7C_4`

Probability of selecting 4 more students from 38 students
`=^(38)C_4`

Probability of having exactly 4 of the students from CS majors

`^7C_4` *
`^(38)C_4`

`35 * 73815\\= 2583525`

2) ) 2 E, 3 CE, 1 AS, 1 M, 1 CS

`^2C_2 * ^(16)C_3* ^4C_1* ^6C_1 * ^7C_1\\= 560 * 4* 6* 7\\= 94080`