Page 182 - DMTH202_BASIC_MATHEMATICS_II

Unit 13: Combinations

In part a above, we observed all probable draws. From that list we only want the ones Notes
that include 1 RED and 2 WHITE marbles.
Let us observe what the draw appears like: we would have to have 1 red and 2 white
marbles to fulfill this condition:
1 RED 2 WHITE
First we are required to find n and r:

Jointly that would make up 1 draw. We are going to have to utilize the counting principle
to assist us with this one.
Note how 1 draw is divided into two parts – red and white. We can not unite them
together since we require a specific number of each one. So we will comprehend how
many ways to get 1 RED and how many ways to get 2 WHITE, and by means of the
counting principle, we will multiply these numbers together.
1 RED:
If n is the number of RED marbles we have to select from, what do you think n is in this problem?

If you said n = 3 you are right!!! There are a total of 3 RED marbles.
If r is the number of RED marbles we are drawing at a time, what do you think r is?
If you said r = 1, pat yourself on the back!! 1 RED marble is drawn at a time.
2 WHITE:

If n is the number of WHITE marbles we have to choose from, what do you think n is in this
problem?
If you said n = 5 you are right!!! There are a total of 5 WHITE marbles.

If r is the number of WHITE marbles we are drawing at a time, what do you think r is?
If you said r = 2, tap yourself on the back!! 2 WHITE marbles are drawn at a time.
Let us place those values into the combination formula and see what we obtain:

n
r
! n *RED: = 3, = 3
C 
n r
r
(n r )! ! *WHITE: = 5, = 2
n
r

3! 5!
C . C  . *Eval. inside ( )
3 1 5 2

( 3 1 1! ( 5 2 2!
)
!

)
!
3! 5 *Expand 3! until it gets to 2!
 .
!
2 1 3 2! *Expand 5! until it gets to 3!
!
!
.
!
.
3 2 5 4 3!
.
 *Cancel out 2!'s and 3!'s
2 1 3 2!
!
!
!
3 5 4
 . .
1 2 1
 3 10
.
 30
If you contain a factorial key, you can put it in as 3!, times 5!, divided by 2!, divided by 1!, divided
by 3!, divided by 2! and then press enter or =.
LOVELY PROFESSIONAL UNIVERSITY 177