Math 30P
Permutations with Restrictions
Permutations with Repetitions
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Many questions require us to deal with some kind of constraint
deal with them FIRST
Ex #1
How many ways can the letters of the word ORANGES be arranged if
a) no restrictions
b) the first letter must be an N
c) the vowels O, A, E must be together
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Ex #2 How many ways can the letters in the word BRAINS be arranged
if the vowels must be together?
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Ex #3: HOw many arragements of the word KITCHEN if the KCN must be
together but not neccesarily in that order
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Ex #4: How many ways can 3 girls, and 4 boys be arranged if no
two people of same gender can sit beside each other
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Ex #5: Six actors and eight actresses are available for a play that
reguires 4 males and 3 females. How many different cast lists
are there?
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Another kind of question involves where a word contains similar letters
How many unique arrangements of word MOM?
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Where there are repetitions of the objects (same letters, make of cars etc ..)
we must use the following formula (not on your formula sheet)
The number of permutations if n objects, where a are the same,
b are the same, c are the same etc.. the formula is:
n!
a!b!c!
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Ex #7 The number of permutations of the word SASKATOON
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Ex#8; How many arrangments of the word POPPIES
a) no restrictions
b) Arrangment begins with a P
c) First two lettters are P
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Ex #9
Brett bought a 10 mini boxes of cereal. 3 are corn flakes,
2 are rice krispies, 1 is coco puffs, 1 is shreddies, and the rest
are raisan bran. Brett plans to eat a box a day. The first mornig he eats
raisan bran
How many different orders for eating are there?
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