1. COMBINATION

2. A combination of a set of distinct objects is an
unordered selection of elements from the set

3. THERE ARE BASICALLY 2 TYPES OF
COMBINATION
COMBINATION WITH
REPETITION
COMBINATION WITHOUT
REPETITION

4. Ex.
Let us say there are five flavors of ice-cream: banana, chocolate, lemon,
strawberry and vanilla. You can have three scoops. How many variations
will there be?
Let's use letters for the flavors: {b, c, l, s, v}
Problem:
How many 3-scoop ice-cream set will be
created out of five flavors?

5. Solution:
Given:
n=5
r=3
= 35

6. CCC SSS BCL
CCB SSB BCS
CCS SSC BCV
BBB CCL LLL SSL VVV BLS BSV
BBC CCV LLB SSV VVB BLV CLS
BBL LLC VVC CLV
BBS LLS VVL VCS
BBV LLV VVS VSL

7. COMBINATION WITH REPETITION:
EX.
How many different 2-letter
words can be created from 4
distinct letters such as a, b, c and
d?

8. where n is the number of things to
choose from, and you choose r of
them
(Repetition allowed, order doesn't
matter)
10

9. AA AA
BB BB
CC CC
DD DD
AB BA
AC CA
AD DA
BC CB
BD DB
CD DC

10. COMBINATION WITHOUT REPETITION
where n is the number of things to
choose from, and you choose r of
them
Given: n=4 (No repetition, order doesn't
r=2 matter)
=6