Combinations, more circular permutations, and permutations of non-distinguishable objects.

1. The difference between
Combinations and
Permutations
The Mastermind by jnthnhys Combination (224365) by Cellach

2. In how many ways can 4 married couples seat themselves
around a circular table if:
(a) spouses sit opposite each other?
(b) men and women alternate?

3. How many different necklaces can be made from 12
beads of different colours?

4. Mom and dad and their 6 children (3 boys and 3 girls)
are to be seated at a circular table. How many ways
can this be done if mom and dad sit together and the
males and females alternate?

5. In how many ways can the student council select 3 people to be on a
subcommittee if there are 7 people on the council.

6. Combination: An arrangement of objects where order does not matter.
Formula: A.K.A the quot;Choosequot; formula.
n is the number of objects to choose from
r is the number of objects to be arranged
is read as quot;n choose rquot;
means: Given a set of n objects, how many different
groups of n objects can be chosen where order does not
matter?

7. Example: How many different tickets can be sold in the 6/49 lottery?
Solution as a Combination
Solution by a Permutation
of Non-Distinguishable
Objects
Number of 49 letter words
made up of 6 Y's and 43 N's

8. Congratulations! You've read
through to the last slide! You
should get some sort of reward or
something, no? Sure you should.
So, here it is. I'll give you quot;the
inside scoop.quot; There's going to be
a quiz tomorrow. Don't tell anyone.
This'll be our little secret: you , me,
and everyone else who actually
reads through all the slides. ;-)