Using generating functions, find a formula for the number of different types of

Question

Using generating functions, find a formula for the number of different types of fruit baskets containing of n pieces of fruit chosen from pomegranates, bananas, apples, oranges, pears, and figs that can be made subject to the following restrictions: • there are either 0 or 2 pomegranates, • there is at least 1 banana, • the number of figs is a multiple of 5, • there are at most 4 pears, and there are no restrictions on the number of apples or oranges. How many ways are there to form such a fruit basket with n = 25 pieces of fruit?

Explanation / Answer

assuming pomegranates as p, bananas as b, apples as a, oranges as o, pears as pe, and figs as f

2p for 0<=p<=1

1+b for 0<=b<=25

5f for 0<=f<=5

pe for 0<=pe<=4

2p +(1+b)+5f+pe <=25

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.