Page 179 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes Let’s put those principles into the combination formula and see what we obtain:
! n
C 
n r *n = 9, r = 2
(n r )!r

9!
C 
9 2 * Eval. inside ()
(9 2)!2!

9!
 * Expand 9! until it gets to 7! which is the larger! in the den.
7!2!
9.8.7!
 * Cancel out 7!’s
7!2!

9.8

2.1
= 36
If you have a factorial key, you can place it in as 9!, divided by 7!, divided by 2! and then press
enter or =.
If you don’t contain a factorial key, you can shorten it as revealed above and then enter it in. It
is most likely best to shorten it first, since in some cases the numbers can get pretty large, and it
would be awkward to multiply all those numbers one by one.
This indicated that there are 36 different games in the conference.

Example: You want to draw 4 cards from a typical deck of 52 cards. How many different
4 card hands are possible?
This would be a combination problem, since a hand would be a group of cards without
considering order.

Observe that if we were putting these cards in any sort of order, then we are required to use
permutations to solve the problem.
But here, order is not an issue, so we will use combinations.

First we are required to find n and r :
If n is the number of cards we have to select from, what do you think n here?
If you said n = 52 you are right!!! There are 52 cards in a deck of cards.
If r is the number of cards we are utilizing at a time, what do you think r is?
If you said r = 4, tap yourself on the back!! We desire 4 card hands.

Let us place those values into the combination formula and see what we obtain:

! n
C 
n r *n = 52, r = 4
(n r )!r

52!
C 
12 4 * Eval. inside ()

(52 4)!4!

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