Question

1. if you have 5 books and you want to know how many different ways you can arrange 3 of them, which formula would you use?

a. 5!
b. c(5,3)
c. (5/3)
d. p(5,3)

Explanation:

Step1: Understand permutation and combination

Permutation \(P(n,r)=\frac{n!}{(n - r)!}\) is for arrangement, combination \(C(n,r)=\frac{n!}{r!(n - r)!}\) is for selection without order. Here we need to arrange 3 books out of 5.

Step2: Analyze each option

• Option a: \(5!\) is the number of arrangements of 5 books, not 3.
• Option b: \(C(5,3)\) is the number of ways to choose 3 books out of 5 (no order), not arrange.
• Option c: \(\binom{5}{3}\) is same as \(C(5,3)\) (combination).
• Option d: \(P(5,3)=\frac{5!}{(5 - 3)!}=\frac{5!}{2!}\) is the formula for arranging 3 books out of 5.

Answer:

d. \(P(5,3)\)