Section 14.1 - Permutations. Permutation – The number of ways to ARRANGE ‘n’ items ‘r’ at...
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Section 14.1 - Permutations
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Transcript of Section 14.1 - Permutations. Permutation – The number of ways to ARRANGE ‘n’ items ‘r’ at...
Section 14.1 - Permutations
Permutation – The number of ways to ARRANGE ‘n’ items ‘r’ ata time with no restriction.
n r
n!
n r
nP n, P P
r !r
0! 1
1! 1
2! 2
3! 6
1
1
2 1
3 2 1
4 3 2 1
5 4 3 2 1
6 5 4 3 2
4! 24
5! 120
16! 720
1
n!n n 1 n 2 n 3 n 4 n
if n 0
5 ... 01if n
n-factorial
How many 469 seven digit phone numbers can there be?
___ ___ ___ ___ ___ ___ ___ 1 1 1 10 10 10 104 6 9 0
123456789
0123456789
0123456789
0123456789
1000
How many license plates are there if it must consist of two letters followed by four non-zero digits?
___ ___ ___ ___ ___ ___ 26 26 9 9 9 9ABCDE…Z
123456789
123456789
123456789
ABCDE…Z
4435236
123456789
How many license plates are there if it must consist of two letters and three digits, with no repetition and the first digitbeing nonzero?
___ ___ ___ ___ ___ 26 25 9 9 8ABCDE…Z
0123456789
0123456789
ABCDE…Z
421200
123456789
How many ways are there to arrange the letters in the wordMATH?
___ ___ ___ ___ 4 3 2 1MATH
MATH
MATH
MATH
24
How many ways are there to arrange the letters in the wordMATH if the T must come first?
___ ___ ___ ___ 1 3 2 1MATH
MATH
MATH
6
MATH
XX
X
How many even three digit numbers are there?(Remember, zero cannot be first in a three digit number)
___ ___ ___ 9 10 50123456789
123456789
0123456789
X
X
X
X
X
450
How many even three digit numbers are there if repetition isnot allowed?
___ ___ ___ 8 8 50123456789
123456789
0123456789
X
X
X
X
X
320
How many six digit numbers are there if no repetition is allowed, and 4 cannot be used?
___ ___ ___ ___ ___ ___ 6 5 4
0123456789
0123456789
53760
123456789
0123456789
0123456789
0123456789
788
Companies whose stocks are listed on the NASDAQ stock exchange have their company name represented by either four or five letters (repetition is allowed). What is the maximumnumber of companies that can be listed on NASDAQ?
___ ___ ___ ___ ___ ___ ___ ___ ___ 26 26 26 26 26ABCDE…Z
ABCDE…Z
ABCDE…Z
ABCDE…Z
ABCDE…Z
ABCDE…Z
ABCDE…Z
ABCDE…Z
ABCDE…Z
26 26 26 26
12338352
In the national league, the pitcher usually hits ninth. If this isthe case, how many batting orders is it possible for a managerto use?
___ ___ ___ ___ ___ ___ ___ ___ ___
P
1
P12345678
8
P12345678
7
P12345678
6 5 4 3 2 1
40320
