Permutations and permutations of non-distinguishable objects.

1. Permutations of
Non-Distinguishable
Objects ... like
but for real
twins. ;-)
this time ...
My Lovely Twins

2. Permutations (the quot;Pickquot; Formula)
A permutation is an ordered arrangement of objects.
n is the number of objects
On the calculator ...
available to be arranged
Press: [MATH]
[<] (Prb)
r is the number of objects
[2] (nPr)
that are being arranged.
Examples:
In how many ways can 5 people In how many ways can six
be seated in a straight line? students be seated in 8 vacant
seats?

3. (a) How many “words” of 4 different letters each can be made from the
letters A, E, I, O, R, S, T?
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(b) How many of these words begin with a vowel and end with a
consonant?
(c) In how many of these words do vowels and consonants alternate?

4. (a) How many numbers of 5 different digits each can be formed from
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the digits 0, 1, 2, 3, 4, 5, 6?
(b) How many of these numbers are even?
(c) What is the probability that one of these numbers is even if the
digits are randomly chosen ?

5. (a) In how many ways can 4 English books and 3 French books be
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arranged in a row on a shelf?
(b) In how many of these ways will the French books be together?
(c) What is the probability the French books will be together?

6. If a fair coin is tossed 4 times, what is the probability of obtaining
exactly 2 heads?

7. T
T
T
T
T
T

8. Permutations of non-distinguishable objects ...
The number of ways to arrange n objects that contain k1, k , k 3, ... sets of
2
non-distinguishable objects is given by:
Examples:
Find the number of different quot;wordsquot; that can be made by rearranging
the letters in the word:
(a) BOOK (b) MISSISSIPPI

10. If a fair coin is tossed 4 times, what is the probability of obtaining
exactly 2 heads?

11. If a fair coin is tossed 4 times, what is the probability of obtaining
exactly 2 heads?

12. All the letters of the word MANITOBA are arranged at random in a
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row. How many ways can this be done?
How many arrangements will have the two A’s next to each other?
What is the probability that this random arrangement will have the two
A’s next to each other?

13. (a) In how many ways can the letters of the word GEOMETRY be
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arranged so that vowels and consonants alternate?
(b) In how many of these ways is Y the last letter?
(c) If one of these quot;wordsquot; is randomly selected, what is the probability
that Y is the last letter?