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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

Respuesta :

Answer:

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

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

Step-by-step 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 = [tex]^7C_4[/tex]

Probability of selecting 4 more students from 38 students [tex]=^{38}C_4[/tex]

Probability of having exactly 4 of the students from CS majors

[tex]^7C_4[/tex] * [tex]^{38}C_4[/tex]

[tex]35 * 73815\\= 2583525[/tex]

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

[tex]^2C_2 * ^{16}C_3* ^4C_1* ^6C_1 * ^7C_1\\= 560 * 4* 6* 7\\= 94080[/tex]

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