Question

1. five cards have different letters written on them. the letters are t, r, a, e, s. the cards are shuffled and laid out on a table with the letters face up next to one another. how many possible arrangements are there? 5 24 50 120

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to find the number of ways to arrange 5 distinct letters. The formula for permutations of \( n \) distinct objects is \( n! \) (n factorial), where \( n! = n\times(n - 1)\times(n - 2)\times\cdots\times1 \).

Step2: Calculate the factorial

Here, \( n = 5 \), so we calculate \( 5! \).
\[
5! = 5\times4\times3\times2\times1 = 120
\]

Answer:

120 (corresponding to the option with "120")