Question

A school committee with 10 members will have representation from the students (S), parents (P), and teachers (T).
A total of 12 students, 8 parents and 7 teachers have been nominated.
a) If there are no restrictions on the committee's structure, show that the total number of different committees that could be elected is 8 436 285
b) Show that the number of randomly selected committee with 5 students, 3 parents and 2 teachers is 931 392.
I don't get matrices at all. :c

Answer 1

a) 12 + 8 + 7 choose 10

Answer 2

27 and 10 in a matrix ?

Answer 3

b) ( 12 choose 5) * (8 choose 3 ) * ( 7 choose 2 )

Answer 4

sorry, what is the matrix method?

Answer 5

\[\left(\begin{matrix}27 \\10\end{matrix}\right)\]
how does this become 8436 285?

Answer 6

or do i not even use matrices? permutation? combination ? how?

Answer 7

The number of combinations of n different objects taken (chosen) rat a time can be represented in several different ways:
\[\large nCr=\left(\begin{matrix}n \\ r\end{matrix}\right)=C(n,\ r)=\frac{n!}{r!(n-r)!}\]

Answer 8

....at a time*

Answer 9

\[ \left(\begin{matrix}27 \\ 10\end{matrix}\right)=\frac{27!}{10! \times (27-10)!}=\frac{27\times26\times25\times24\times23\times22\times21\times20\times19\times18}{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}\]