1. More examples on perms and combs

2. exercise
How many ways can a photographer at a wedding arrange 6 people
in a row from a group of 10 people, where the bride and groom are
among those people, such that
(a) the bride is in the picture
(b) the bride and the groom are in the picture
(c) either the bride is in the picture or the groom is in the picture,
but not both

3. exercise
How many ways can a photographer at a wedding arrange 6 people
in a row from a group of 10 people, where the bride and groom are
among those people, such that
(a) the bride is in the picture
The bride can be in one of 6 positions
we then have 5 positions to permute from 9 people
P(n,r) where n=9 and r=5
9!/(9-5)!
therefore there are ways to do this
90720

4. exercise
How many ways can a photographer at a wedding arrange 6 people
in a row from a group of 10 people, where the bride and groom are
among those people, such that
(b) the bride and the groom are in the picture
The bride can be in one of 6 positions and the groom in one of 5 (or vice versa)
30 alternatives in all
we then have 4 positions to permute from 8 people
P(n,r) where n=8 and r=4
8!/(8-4)!
therefore there are ways in total
50400

5. exercise
How many ways can a photographer at a wedding arrange 6 people
in a row from a group of 10 people, where the bride and groom are
among those people, such that
(c) either the bride is in the picture or the groom is in the picture,
but not both
consider the bride without the groom
the bride can be in one of 6 positions
the remaining 5 positions can be taken by 8 people
i.e. 8 guests, not the groom!
P(n,r) where n=8 and r = 5
8!/(8-5)!
in total there are ways to have the bride without the groom
40320 ways
The same holds for the groom without the bride
therefore = ways in total

6. exercise
In 3d year, single honours, students must take 9 modules
with 9 exams (I’m ignoring the team project in this discussion).
Each module has the following exam structure
How many different ways can
you satisfy the above requirements?

7. fin