# Permutations Question

• Sep 14th 2009, 04:33 PM
MATHDUDE2
Permutations Question
Hi, I'm having trouble with this question. Can anyone explain how to do it?

A students' council executive could consist of a president, vice-president, secretary, treasurer, social convenor, fundraising chair, and four grade representatives. Suppose ten students have been nominated to fill these positions. Five of the nominees are from grade 12, three are from grade 11, and the other two are a grade 9 and a grade 10.

In how many ways can the council be schosen if the president and vice-president must be grade 12 students and the grade representatives must represent their current grade level?

The answer at the back of the book is: 4320

Thanks!!
• Sep 14th 2009, 05:50 PM
Robb
From the 5 grade 12 you must select 1 year rep, 1 president and 1 vice president.
From 3 grade 11, you must select 1 year rep
From 1 grade 10, you must select 1 year rep
From 1 grade 9, you must select 1 year rep.
This leaves 4 students to get the secretary position
Once the secretary position has been selected, levaes 3 students to get the treasurer position
Once the treasurer position selected, leaves 2 students from the social convenor
And then finally, the last student must get the fundraising chair. So;

$\left( \begin{array}{cc}5\\1\end{array}\right) \cdot \left(\begin{array}{cc}4\\1\end{array}\right)$ $\cdot \left(\begin{array}{cc}3\\1\end{array}\right) \cdot \left(\begin{array}{cc}3\\1\end{array}\right)$ $\cdot \left(\begin{array}{cc}1\\1\end{array}\right) \cdot \left(\begin{array}{cc}1\\1\end{array}\right) \cdot \left(\begin{array}{cc}4\\1\end{array}\right) \cdot \left(\begin{array}{cc}3\\1\end{array}\right)$ $
\cdot \left(\begin{array}{cc}2\\1\end{array}\right) \cdot \left(\begin{array}{cc}1\\1\end{array}\right) = 4320$
• Sep 14th 2009, 06:49 PM
MATHDUDE2
Thanks!!!