Question

Keely is planning a bridal shower for her best friend. At the party, she wants to serve 4 beverages, 3 appetizers, and 4 desserts, but she does not have time to cook. She can choose from 11 bottled drinks, 10 frozen appetizers, and 8 prepared desserts at the supermarket. How many different ways can Keely pick the food and drinks to serve at the bridal shower?

Answer 1

The different ways in which Keely can pick the food and drinks to serve at the bridal shower is 2,772,000.

Explanation:

Combinations is a mathematical procedure to determine the number of ways to select k items from n different items, without replacement and irrespective of the order of selection.

The formula to compute the combination of k items from n items is:

`{n\choose k}=(n!)/(k!(n-k)!)`

The menu for the bridal shower consists of:

Beverages: 4

Appetizers: 3

Dessert: 4

It is provided that Keely does not have time to cook. SO she goes to the supermarket and there she has the following options:

Beverages: 11

Appetizers: 10

Dessert: 8

Compute the number of ways Keely can select 4 beverages from 11 bottled drinks as follows:

`{n\choose k}=(n!)/(k!(n-k)!)`

`{11\choose 4}=(11!)/(4!(11-4)!)`

`=(11!)/(4!* 7!)`

`=(11* 10* 9* 8* 7!)/(4!* 7!)`

`=330`

Keely can select 4 beverages in 330 ways.

Compute the number of ways Keely can select 3 appetizers from 10 frozen appetizers as follows:

`{n\choose k}=(n!)/(k!(n-k)!)`

`{10\choose 3}=(10!)/(3!(10-3)!)`

`=(10!)/(3!* 7!)`

`=(10* 9* 8* 7!)/(3!* 7!)`

`=120`

Keely can select 3 appetizers in 120 ways.

Compute the number of ways Keely can select 4 desserts from 8 prepared desserts as follows:

`{n\choose k}=(n!)/(k!(n-k)!)`

`{8\choose 4}=(8!)/(4!(8-4)!)`

`=(8!)/(4!* 4!)`

`=(8* 7* 6* 5* 4!)/(4!* 4!)`

`=70`

Keely can select 4 desserts in 70 ways.

Compute the total number of ways in which Keely can select 4 beverages, 3 appetizers, and 4 desserts for the party as follows:

Total number of ways = n (4 beverages) × n (appetizers) × n (dessert)

`={11\choose 4}* {10\choose 3}* {8\choose 4}`

`=330* 120* 70\\=2772000`

Thus, the different ways in which Keely can pick the food and drinks to serve at the bridal shower is 2,772,000.