Question

of the 15 students who solved the challenge question in mathematics contest. 8 were enrolled in mathematics of data mangement. Five of the solutions are selected at random for a display

a) Prepare a table of the probablility distribution for thenumber of solutions in the display that were prepared by mathematics of data students.

Answer 1

the possible number of students selected from the 8 enrolled in data management are
x = 0
x = 1
x= 2
x = 3
x = 4
x = 5

the number of ways to select none is
\[P(x=0)=\frac{7\times 6\times 5\times 4\times 3}{\dbinom{15}{5}}\]

Answer 2

\[P(x=1)=\frac{\dbinom{8}{1}\times \dbinom{7}{4}}{\dbinom{15}{5}}\]
that is the number of ways to choose one from the 8 times the number of ways to choose 4 from the other seven, divided by total number of ways to choose 5 from 15

others are similar

Answer 3

Why is it only up to x=5? Why not x=8? since there are 8 people?