This document discusses two types of combinations: combinations with repetition and combinations without repetition. Combinations with repetition allow elements to be chosen multiple times from a set, while combinations without repetition do not allow repeats. It provides examples to illustrate each type, such as how many 2-letter words can be created from 4 letters with repetition (10 combinations) versus without repetition (6 combinations). The key difference between the two types is whether repetition of elements is allowed or not when selecting elements from a set.

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