In the game of Jumble, the letters of a word are scrambled. The player must form the correct word. In a recent game in a local newspaper, the Jumble “word” was LINCEY. How many different arrangements are there of the letters in this “word”?

Verified step by step guidance

1. Identify the total number of letters in the word. Here, the word is "LINCEY," which has 6 letters.
2. Check if any letters are repeated. Since all letters in "LINCEY" are distinct, there are no repetitions.
3. Recall the formula for the number of different arrangements (permutations) of n distinct letters: \(n!\) (n factorial), which means the product of all positive integers from 1 to n.
4. Apply the formula to the word "LINCEY" by calculating \$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$.
5. The result from the factorial calculation gives the total number of different arrangements of the letters in the word.

Key Concepts

Permutations of Distinct Objects

Permutations refer to the number of ways to arrange a set of distinct objects in order. When all objects are unique, the total number of arrangements is the factorial of the number of objects, denoted as n!. For example, 6 distinct letters can be arranged in 6! ways.

Factorial Function

The factorial of a positive integer n, written as n!, is the product of all positive integers from 1 to n. It is used to calculate permutations and combinations. For instance, 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Identifying Unique Letters

Before calculating permutations, it is important to check if any letters repeat. Repeated letters reduce the total number of unique arrangements. In this problem, all letters in 'LINCEY' are distinct, so no adjustment for duplicates is needed.