permutations combinations1
TRANSCRIPT
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8/17/2019 Permutations Combinations1
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10.3 – Using Permutations and Combinations
Permutation: The number of ways in which a subset of objects
can be selected from a gien set of objects! where order is
im"ortant.
Combination: The number of ways in which a subset of
objects can be selected from a gien set of objects! where
order is not im"ortant.
#ien the set of three letters! $%! &! C'! how many "ossibilities are there
for selecting any two letters where order is im"ortant(
)%&! %C! &C! &%! C%! C&*
#ien the set of three letters! $%! &! C'! how many "ossibilities are there
for selecting any two letters where order is not im"ortant(
)%&! %C! &C*.
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10.3 – Using Permutations and Combinations
+actorial +ormula for Permutations
,.
) *,n r
n P
n r
=
−
+actorial +ormula for Combinations
,.
, ,) *,
n r n r
P nC
r r n r
= =
−
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10.3 – Using Permutations and Combinations
-aluate each "roblem.
c* P a*/ P
3
b* /C 3 d* C
5⋅4⋅3
60
10
720 1
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10.3 – Using Permutations and Combinations
ow many ways can you select two letters followed by three
digits for an 2 if re"eats are not allowed(
Two "arts:
. 2etermine the set of three digits.1. 2etermine the set of two letters.
P 10 P 3
26⋅25
650
10⋅9⋅8
720
650⋅720468,00
0
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10.3 – Using Permutations and Combinations
% common form of "o4er inoles hands )sets* of fie cards each! dealt
from a dec4 consisting of / different cards. ow many different /5card
hands are "ossible(int: 6e"etitions are not allowed and order is not im"ortant.
/C /
2,598,960 5-cardhands
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10.3 – Using Permutations and Combinations
+ind the number of different
subsets of si7e 3 in the set:
$m, a, t, h, r, o, c, k, s'.
+ind the number of arrangements
of si7e 3 in the set:
$m, a, t, h, r, o, c, k, s'.
8C 3
84 Diferentsubsets
8 P 3
9⋅8⋅7
504 arrangements
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10.3 – Using Permutations and Combinations
#uidelines on 9hich ethod to Use