Question

Calculate the following quantities.

a. C(1,0) and C(1,1)
b. C(2,0), C(2,1), and C(2,2)
c. C(3,0), C(3,1), C(3,2), and C(3,3)
d. C(4,0), C(4,1), C(4,2), C(4,3), and C(4,4)

Answer 1

By definition: 0! = 1 and 1! = 1

a. C (1,0) = 1!/1!.0! = 1

C (1,1) = 1!/1!.0! = 1

b. C(2,0) = 2!/2!.0! = 1

C(2,1) = 2!/1!.1! = 2

C(2,2) = 2!/2!.0! = 1

c. C(3,0) = 3!/3!.0! = 1

C(3,1) = 3!/1!.2! = 3

C(3,2) = 3!/1!.2! = 3

C(3,3) = 3!/3!.0! = 1

d. C(4,0) = 4!/0!.4! = 1

C(4,1) = 4!/3!.1! = 4

C(4,2) = 4!/2!.2! = 6

C(4,3) = 4!/3!.1! = 4

C(4,4) = 4!/4!0! = 1

Explanation:

Answer 2

Answer and Step-by-step explanation:

By definition: 0! = 1 and 1! = 1

a. C (1,0) = 1!/1!.0! = 1

C (1,1) = 1!/1!.0! = 1

b. C(2,0) = 2!/2!.0! = 1

C(2,1) = 2!/1!.1! = 2

C(2,2) = 2!/2!.0! = 1

c. C(3,0) = 3!/3!.0! = 1

C(3,1) = 3!/1!.2! = 3

C(3,2) = 3!/1!.2! = 3

C(3,3) = 3!/3!.0! = 1

d. C(4,0) = 4!/0!.4! = 1

C(4,1) = 4!/3!.1! = 4

C(4,2) = 4!/2!.2! = 6

C(4,3) = 4!/3!.1! = 4

C(4,4) = 4!/4!0! = 1