Question

1. assume that 22 kids have their names (all different) put into a hat. the teacher is drawing 5 names to see who will speak first, second, etc., for the day. how many permutations of names can the teacher draw?

$5^{22}$
$22!$
$\frac{22!}{17!}$
$22^{5}$

Explanation:

Step1: Recall Permutation Formula

The permutation formula for choosing \( r \) items from \( n \) items (where order matters) is \( P(n, r)=\frac{n!}{(n - r)!} \). Here, \( n = 22 \) (total kids) and \( r = 5 \) (names drawn).

Step2: Substitute Values

Substitute \( n = 22 \) and \( r = 5 \) into the formula: \( P(22, 5)=\frac{22!}{(22 - 5)!}=\frac{22!}{17!} \).

Answer:

\(\frac{22!}{17!}\) (the option with \(\frac{22!}{17!}\))