Question

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. ( p(5,3) )
b. ( \binom{5}{3} )
c. ( c(5,3) )
d. ( 5! )

Explanation:

• Permutation formula: The permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\) is used when we want to find the number of ways to arrange \(r\) objects out of \(n\) objects where the order of arrangement matters. Here, \(n = 5\) (total number of books) and \(r=3\) (number of books to be arranged).
• Combination formula: The combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\) (also written as \(\binom{n}{r}\)) is used when we want to find the number of ways to select \(r\) objects out of \(n\) objects where the order of selection does not matter. Since we are arranging the books (order matters), combination formula is not appropriate.
• Factorial formula: \(n!\) gives the number of ways to arrange \(n\) distinct objects. Here we are not arranging all \(5\) books, so \(5!\) is not relevant.

Answer:

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