Question

1. -/1 points details my notes ask your teacher practice another a student is given a reading list of nine books from which he must select two for an outside reading requirement. in how many ways can he make his selections? ways resources ebook submit answer 8. -/1 points details my notes ask your teacher practice another a group of four students studying for a bar exam has formed a study group. each member of the group will be responsible for preparing a study outline for one of four courses. in how many different ways can the four courses be assigned to the members of the group? ways resources ebook

Explanation:

Step1: Use combination formula (order doesn't matter)

For problem 7: The number of ways to choose 2 books from 9 is given by the combination formula $C(n,k)=\frac{n!}{k!(n-k)!}$, where $n=9$, $k=2$.
$\frac{9!}{2!(9-2)!}=\frac{9\times8\times7!}{2\times1\times7!}$

Step2: Simplify the combination expression

Cancel out $7!$: $\frac{9\times8}{2\times1}=36$

Step3: Use permutation formula (order matters)

For problem 8: Assigning 4 courses to 4 students is a permutation, $P(n,n)=n!$, where $n=4$.
$4!=4\times3\times2\times1$

Step4: Calculate the permutation value

$4\times3\times2\times1=24$

Answer:

Problem 7: 36 ways
Problem 8: 24 ways