Question

1. 3.38 / 6.76 points a restaurant provides a brunch where the omelets are individually prepared. each guest is allowed to choose from 10 different ingredients. a student has been asked to form the following sets. determine the (a) how many different types of omelets can the restaurant prepare? (b) what is the minimum number of ingredients that must be available if the restaurant wants to advertise that it offers over 4,000 different omelets? learn it: determine the number of subsets within a set. learn it: apply polya model to solve problems. resources read it watch it tutorial

Explanation:

Step1: Calculate total subsets (omelets)

Each ingredient can be either included or excluded, so for $n$ ingredients, the total number of subsets (including the empty set, which represents a plain omelet) is $2^n$. For $n=10$:
$$2^{10} = 1024$$

Step2: Solve for minimum $n$ (over 4000)

Find the smallest integer $n$ where $2^n > 4000$:

• $2^{11}=2048$, $2^{12}=4096$

Since $4096 > 4000$, $n=12$.

Answer:

(a) 1024
(b) 12