i.e of one kindjmiglior/m10120F20 lectures...i.e 3 ofone kind 2 ofanother e.g 3 kings too 7 s Nole...

EI Howmany pokerhands are full housei.e 3 of one kind 2 ofanother e.g

3 kings too 7 s

Nole the kings and the 7 s play differentroles thekings are

what we have two of

To put anotherway 3kings two sevens is differentfromthreesevens

2 kings

Stept decide whichof the 13denominationsyouhave 3of andwhich

you have 2 oforder is important

13 12

have3of have2ofP 13,2 ways for step1

Step decide which 3 and which 2 order is not important1

CC4,37 44,2

aus P 13,2 CC4,3 4,2 3744

Ey Howmanypolarhands contain two pairs e.g KO KB 7 753 8D

fromdifferentdenominationsC 13,2 cc4,2 CC4 2 a 444 1

fix Redothegridexample

A

BHowmany paths go from A to B movingonlyR or D

9 blocks exactly 4 ofwhich are D

Choose which 4 of 9 are D andthen therest are R

91 49.41 41 itfix A clubhas 5 men 6 women they have to choosepres VPtreasurer

a In howmanyways can theymakethesechoicesi i e i if at least oneofthethreebhas to be a woman

and11 to 9 P 11 3al

all menpres VP treas

b p 11,3 P 5,3 PCT31 5 4 3pres UP treas

I e insteadofdoing it directly verycomplicated

we throw out fromthe PC 3 those which

doit satify the condition PCs31

EI Themathclubhas 10members

chess 8

juggling 12

No one belongs to more than one club total of 30people

Theuniversity wants to send 3 clubmembers to a convention

In howmanyways can theychoosethe3 if

it doesn'tmatterwhatclubthey belongto CC30,31

b it has tobe one fromeach club 4191 c 8,1 CCR i

El all 3 have to befromthe sameclub Clio3 t 48 3 t c CR3

d not all can be from thesame club

aus to Cal fans to Cal CC30,3 ch93 cc8,3 Ccr 31

An urn contains 8 greenballs are 6 blueballs distinguishable

You choose 5 In howmany ways can youchoosethe 5 so that there

are more green balls than blue ones

G Bi 5 O C 8,5 46,04 I C 8,4 46,13 2 ace3 age

add these three

Howmany poker hands consistofa 9 lo J Q K of the same suit

b 9 co J Q K of positslydifferentsuits

cat 45

s 4 4 4 4 4 4q is J Q K