Upper%Bicutan%National%High%School%
Gen.%Santos%Ave%Central%Bicutan%Taguig%City%
Third%Quarter%
Mathematics*10*
LEARNING(ACTIVITY(SHEET(
!
!
Permutation%
is* an* arrangement," or* listing,* of* objects* in* which* the* order* is* important
.
*Each* possible* arrangement* is* a*
permutation.*The*number*of*permutations*is*given*for*the*following*cases:**
!
!
*
!
*
*
Simplify*P(15,3)*=*__* * * * *
👍
Your*Turn.**Practice*only.*
P(15,3)*=*
!!
(
!$%
)
!
(=(
𝟏𝟓!
(
𝟏𝟓$𝟑
)
!
((
************=(
*𝟏𝟓!*
*+,!*
(=(
*𝟏𝟓*•*+𝟒*•*+𝟑*•*+𝟐!*
*+,!*
(=(15•14•13*
P(15,3)*=*2*730*
****Simplify:*
1.**P(9,5)*=*__********************3.**P(n,3)*=*990***n=___*
2.**6P6*=*___**********************4.**P(6,r)*=*360.***r=*___*
!
!
PROBLEM-SOLVING*ON**PERMUTATIONS*
!
!
ACTIVITY*1.*
Evaluate*the*following*permutations*using*
*P(n,r)*=*
𝐧!
(𝐧$𝐫)!.*Write*your*complete*solutions*inside*the*box.*
!!!!
ACTIVITY!3.!
Solve!the!following!situations.!Write!your!complete!solutions.!
1.*A*teacher*wants*to*assign*4*different*tasks*to*her*4*
students.*In*how*many*possible*ways*can*she*do*it?*
*
*
*
*
4.*In*how*many*ways*can*you*arrange*8*different*can*goods*on*
a*shelf?*
*
2.*In*how*many*different*ways*can*5*bicycles*be*parked*if*there*
are*7*available*parking*spaces?*
*
!
%
*
5.**A*baseball*coach*is*going* to*pick* 8*players* from*a* baseball*
squad*of*16*to*take*turn*batting*against*the*pitcher.*How*many*
batting*orders*are*possible?*
3.* There* are* 8* basketball* teams* competing* for* the* top* 4*
standings* in* order* to* move*up* to* the* semi-finals.* Find* the*
number*of*possible*rankings*of*the*four*top*teams.*
"
(
6.*How* many* three*letter*words* (including* nonsense*words)*
can*you*make*from*the*letters*of*the*English*alphabet,*if*letters*
cannot*be*repeated?*
*
Name:
*_______________________________________*
Section:
*_____________*
Score:
*_______*
Lesson/Topic:*
Permutation*(taken*at*a*time/all*at*time)***************************************************************************************************************
*
Seatwork*#:*
__________*
Date:
*_________*
!
Taken*at*
a
*time*
P(n,r)*=!
𝐧!
(𝐧h𝐫)!,!
n*
≥
*r*
Where:*
n*=*total*number*of*objects*
r*=*number*of*arrangements*
(choices)*
ü Winners*in*a*contest*
ü Entering*PIN*in*ATM*
ü Lining*up*in**row*for*a*
group*picture*
Taken*
all
*at*a*
time*
P(n,*n)*=*n!*
A.*TAKEN*AT*A*TIME.**
∆*
∑*
Ω*
Ꝋ*
ꞵ*
****Suppose*we*have* 5*different* math*symbols,*and*we*wish*
to*arrange*3*of*them*in*a*row.*In*how*many*ways*can*be*this*
done?**********
**
*P(n,r)*=*
𝐧!
(𝐧$𝐫)!
((((
Where*n*=*5,*r*=*3*
*** 𝟓!
(𝟓$𝟑)!
(
=
((
𝟓!
𝟐!
(
=
(
𝟓*•*𝟒*•*𝟑*•*𝟐!
𝟐!
(
=
(
𝟓*•*𝟒*•*𝟑*•*𝟐!
𝟐!
(=*
5•4•3*=*
60
*
**%%%P(5,3)%=%60*
B.*TAKEN*ALL*A*TIME.
**
!
"
"
"
"
*****In*how*many*ways*can*4*persons*arrange*themselves*in*a*
row*for*picture*taking?***
*
******P(n,*n)*=*
𝐧!((((((Where*n*=*4
(
********P(4,4)*=*4!**
*********************=*
4•3•2•1**=*
24*
********P(4,4)*=*24*
1.***P*(10,*4)*=*___*
*
%
3.*P*(9,*6)*=*___* *
5.*P(
n
,*4)*=*840*
2.**P(8,8*)*=*____*
4.**P(15,*3)*=*___**
*
!
6.**P(9,*
r
)*=*504*
