Question

6. A group of 10 students is in a club. There are 4 leadership positions in...

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.)

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Answer #1

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:

n! nPrin-r!

10! 10 P4 = (10-4)!

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

TI-84 Plus Silver Edition TEXAS INSTRUMENTS MATH NUM CPX PRE 1:rand Zonpr Sincr 4:! 5: rand Intc 6: randNorm 7+randBinc STAT

5) Now press number 4

TI-84 Plus Silver Edition TEXAS INSTRUMENTS 10 nr 4 STAT PLOT 1 TBLSETE2 FORMAT ESCALC F4 TABLE F5 WINDOW ZOOM TRACE GRAPH 2N

Thus we will see like above.

6) Press Enter

thus we get answer : 5040

that is:

10P4 = 5040

We can solve this manually :

10! 10 P4 = (10-4)!

10 P4 = 1

10 x 9 x 8 x 7 x 6! 10 P4 = ?

10 P4 = 10 x 9 x 8 x 7

10 P4 = 5040

Thus there are 5040 ways for  4 different leadership positions to be filled by those 10 students.

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