Respuesta :
We have 18 students,
There are 11 math majors and 7 computer science majors.
We need to find the probability that randomly selecting four persons in the group will result in three math majors and 1 computer science major.
Now,
For select 3 math majors of 11, we use a combination:
11C3
Where the formula is given by:
[tex]\text{nCr}=\frac{n!}{(n-r)!r!}[/tex]Where n is the number of the total group and r the sample:
Then:
[tex]11C3=\frac{11!}{3(11-7)!}=165[/tex]Now, for the selection 1 computer science major of 7:
n=7 and r=1
[tex]7C1=\frac{7!}{1!(7-1)!}=7[/tex]Now, the selection 4 persons of the group of 18 students:
18C4, where n=18 and r=4
[tex]18C4=\frac{18!}{4!(18-4)!}=3060[/tex]The probability of the chose three math majors and 1 computer science major, is given by:
[tex]P=\frac{7C1\cdot11C3}{18C4}=\frac{7\cdot165}{3060}[/tex]Therefore:
[tex]P=0.38[/tex]