Now suppose that you have 2 individual and identical oranges. Give a generating function for selecting from the oranges. (f) Suppose you add the oranges to the set of apples and bananas. Give the generating function for the combined set. (g) How many ways are there to select three pieces of fruit from the set of apples, bananas and oranges

C (2, r)

C (6, r)

20 ways

Step-by-step explanation:

(a) Selection can be dependent on whether there is order or not. Assume there is no order of selection, the function is given by

Selection = C (n, r) ... (1)

Selection = C (2, r)

Where C is a combination function, n is the number of oranges and is the number of oranges selected at a time.

Assuming 1 at a time

Selection = 2C1 = 2! = 2 ways

(f) For the combination of oranges, banana and apples. We assume the apples and banana are identitcal to each other as the the oranges and are of the same number

n = 6, n (O) = 2, n (B) = 2, n (A) = 2

Selection = C (n, r)

= C (6, r)

(g) Selection = C (6, 3)

Selection = 6C3 = [6 * 5 * 4 * 3!]/3!3!

= (6*5*4) / 3*2

= 20ways