6. A group of 10 students is in a club. There are 4 leadership
positions in the club
(President, Vice President, Secretary, Treasurer). In how many ways
can those 4 different leadership
positions be filled by those 10 students? (You can use a calculator
probability command, but show
what you are doing on your calculator.)
Solution:
Given:
n = total students = 10
r = Number of position to fill (President, Vice President, Secretary, Treasurer) = 4
Since order is important , we use permutation.
Thus we use formula:
We use following step in TI 84 plus calculator
1) Press Number 10
2) Click on MATH
3) Select PRB
4) Under PRB select nPr
5) Now press number 4
Thus we will see like above.
6) Press Enter
thus we get answer : 5040
that is:
10P4 = 5040
We can solve this manually :
Thus there are 5040 ways for 4 different leadership positions to be filled by those 10 students.
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