Question

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.)

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 PLOTF1 TBLSETF2 FORMAT F3 CALC F4 WINDOW STOOM TRACE TABLE F5 GRAPH 2ND MODE DEL WIDE ALPHA LINE X.T.O.n STAT MATH APPS CLEAR PRGM VARS VARS CLEAR

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 2ND ALPHA MATH THIẾT APPS KẾ T PRGM HI VARS CLEAR

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.