Question

: Planning a summer study schedule About Susan plans on studying four different subjects (Math, Science, French, and Social Studies) over the course of the summer. There are 100 days in her summer break and each day she will study one of the four subjects. A schedule consists of a plan for which subject she will study on each day (a) How many ways are there for her to plan her schedule if there are no restrictions on the number of days she studies each of the four subjects? (b) How many ways are there for her to plan her schedule if she decides that the number of days she studies each subject will be the same?

Answer 1

Answer:

Part (A): The total number of ways are $4^{100}$

Part (B): The total number of ways are $1.6122075076\times10^{57}$

Step-by-step explanation:

Consider the provided information.

Part(A) a) How many ways are there for her to plan her schedule if there are no restrictions on the number of days she studies each of the four subjects?

She plans on studying four different subjects.

That means she has 4 choices for each day also there is no restriction on the number of days.

Hence, the total number of ways are:

$4\times 4\times4\times4\times......4=4^{100}$

Part (B) How many ways are there for her to plan her schedule if she decides that the number of days she studies each subject will be the same?

She wants that the number of day she studies each subject will be the same that means she studies for 25 days each subject.

Therefore, the number of ways are:

$^{100}C_{25}\times ^{75}C_{25}\times ^{50}C_{25}\times ^{25}C_{25}=1.6122075076\times10^{57}$