week 3

Question 1

n!

Answer 1

n factorial
n x (n-1)!
eg 4! = 4x3x2x1

Question 2

0!

Answer 2

1

Question 3

1!

Answer 3

1

Question 4

2!

Answer 4

2

Question 5

3!

Answer 5

6

Question 6

4!

Answer 6

24

Question 7

5!

Answer 7

120

Question 8

circular permutations
number of ways n objects can be arranged around a circle

Answer 8

(n-1)!

Question 9

(n k)

Answer 9

number of ways to select k objects from a set of n objects

= n!/k!(n-k)!

Question 10

(0 0)

Answer 10

1

Question 11

(1 0)

Answer 11

1

Question 12

(1 1)

Answer 12

1

Question 13

(2 0)

Answer 13

1

Question 14

(2 1)

Answer 14

2

Question 15

(2 2)

Answer 15

1

Question 16

(3 0)

Answer 16

1

Question 17

(3 1)

Answer 17

3

Question 18

(3 2)

Answer 18

3

Question 19

(3 3)

Answer 19

1

Question 20

(4 0)

Answer 20

1

Question 21

(4 1)

Answer 21

4

Question 22

(4 2)

Answer 22

6

Question 23

(4 3)

Answer 23

4

Question 24

(4 4)

Answer 24

1

Question 25

(n 0)

Answer 25

1
there is 1 way to choose 0 objects ( don’t choose any)

Question 26

(n 1)

Answer 26

n
there are n ways to choose 1 object

Question 27

(n n)

Answer 27

1
there is 1 way to choose n objects ( choose all of them)

Question 28

(n k)

Answer 28

(n n-k)
eg (5 2) = (5 5-2) (5 3)

Question 29

selecting k objects from a set of n objects and arranging around the k objects

Answer 29

n!/ (n-k)!

Question 30

selecting k objects from a set of n objects and arranging around the k objects in a circle

Answer 30

1/k n!/k(n-k)!