Consider the situation in Example 9.6.2.
a. Suppose the store has only six cans of lemonade but at leant 15 can of each of the other four types of soft drink. In how many dif-
ferent ways can fifteen cans, of soft drink be selected?
b. Suppose that the store has only five cans of root beer and only six cans of lemonade but at least 15 cans of each of the other three types of soft drink. In how mam different ways can fifteen cans of soft drink be selected?

(a)

To find:

The number of different ways that the 15 cans can be chosen.

When six cans are already lemonade.

Given information:

Given 5 different types and to select 15 cans when six are already lemonade.

Formula Used:

When there are certain number of elements n need to be selected

from the given number of different kinds k

( n+k−1n)=(n+k−1)!n!(k−1)!

Calculation:

To select the six cans of lemonade =6! =6*5*4*3*2*1= 720

Then to select the balance 9 cans from the four type

(b)

To find:

The number of different ways that the 15 cans can be chosen.

When having six cans of lemonade and five cans of root beer.