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

Answer:

Total number of required ways = 18480

Step-by-step 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:

$_nC_r = \dfrac{n!}{(n-r)!r!}$

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:

$_{11}C_9\ or\ _{11}C_2 = \dfrac{11 \times 10}{2} = 55$

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

$_{8}C_3= \dfrac{8 \times 7 \times 6}{6} = 56$

Number of ways to select 2 desserts out of 4:

$_{4}C_2= \dfrac{4 \times 3}{2} = 6$

Total number of ways = $55 \times 56 \times 6$ = 18480