Respuesta :
Answer:
The different ways in which Keely can pick the food and drinks to serve at the bridal shower is 2,772,000.
Step-by-step 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:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
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:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
[tex]{11\choose 4}=\frac{11!}{4!(11-4)!}[/tex]
[tex]=\frac{11!}{4!\times 7!}[/tex]
[tex]=\frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]
[tex]=330[/tex]
Keely can select 4 beverages in 330 ways.
Compute the number of ways Keely can select 3 appetizers from 10 frozen appetizers as follows:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
[tex]{10\choose 3}=\frac{10!}{3!(10-3)!}[/tex]
[tex]=\frac{10!}{3!\times 7!}[/tex]
[tex]=\frac{10\times 9\times 8\times 7!}{3!\times 7!}[/tex]
[tex]=120[/tex]
Keely can select 3 appetizers in 120 ways.
Compute the number of ways Keely can select 4 desserts from 8 prepared desserts as follows:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
[tex]{8\choose 4}=\frac{8!}{4!(8-4)!}[/tex]
[tex]=\frac{8!}{4!\times 4!}[/tex]
[tex]=\frac{8\times 7\times 6\times 5\times 4!}{4!\times 4!}[/tex]
[tex]=70[/tex]
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)
[tex]={11\choose 4}\times {10\choose 3}\times {8\choose 4}[/tex]
[tex]=330\times 120\times 70\\=2772000[/tex]
Thus, the different ways in which Keely can pick the food and drinks to serve at the bridal shower is 2,772,000.
