Question

A catering service offers 11 appetizers, 8 main courses, and 4 desserts. A customer is to select 9 appetizers, 3 main courses, and 2 desserts for a banquet. In how many ways can this be done?

Answer 1

Total number of required ways = 18480

Explanation:

Given that

Total appetizers = 11

Total main courses = 8

Total desserts = 4

To be selected 9 appetizers

3 main courses and

2 desserts.

To find:

Number of ways of selecting them.

Solution:

Number of ways to select 'r' number of items out of 'n' number of items is given as:

`_nC_r = (n!)/((n-r)!r!)`

One important property:

`_nC_r = _nC_(n-r)`

Here we have 3 items, we will find each items' number of ways of selecting and then will multiply all of them.

Number of ways to select 9 appetizers out of 11 appetizers:

`_(11)C_9\ or\ _(11)C_2 = (11 * 10)/(2) = 55`

Number of ways to select 3 out of 8 main courses:

`_(8)C_3= (8 * 7 * 6)/(6) = 56`

Number of ways to select 2 desserts out of 4:

`_(4)C_2= (4 * 3)/(2) = 6`

Total number of ways =
`55 * 56 * 6` = 18480