COMBINATIO
N
Combination
-an arrangement of
objects where order
does not matter
Combination Formula
Problem-Solving
Involving
Combination
In how many ways can 5
students be chosen from a
group of 20 to attend the World
Youth Day celebration?
COMBINATION
PROBLEM
A basketball coach has 5
guards and 7 forwards on
COMBINATION
PROBLEM
his basketball team. In how
many different ways can he
select a starting team of 2
guards and 3 forwards?
In a group of 6 boys and 4
girls, four children are to be
COMBINATION
PROBLEM
selected.
In
how
many
different ways can they be
selected
such
that
at
least one boy should be
there?
We may have (1 boy and 3 girls) or
(2 boys and 2 girls) or (3 boys and
1 girl) or (4 boys).
Required number of ways
SOLUTION
=(6C1×4C3 )+(6C2×4C2 )+
(6C3×4C1 )+6C4
=24+90+80+15=209
A committee of 7 has to be formed
from 9 boys and 4 girls. In how many
ways can this be done when the
COMBINATION
PROBLEM
committee consists of:
(i) exactly 3 girls?
(ii) at least 3 girls?
(iii) at most 3 girls?
DECK OF CARDS
Poker is a card game played
from a deck of 52 cards.
COMBINATION
PROBLEM
a.) How many different five-
card
poker
possible?
hands
are
b.) In how many hands in a.)
will there be:
COMBINATION
PROBLEM
i.
All diamonds?
ii.
4 black cards and 1 red
card?
iii. 3 kings and 2 queens?
iv. 3 kings?
v. 4 aces?