76,678 views
17 votes
17 votes
How many different ways

can you arrange the letters
in the word SMILE?


PLSSS HELP

User Rasmus Puls
by
3.3k points

1 Answer

12 votes
12 votes

Answer:

120 different ways

Explanation:

The formula to count the permutation since the order the matters: nPr = n! / (n - r)!, where n is the total number and r is the total number of chosen.

1) Substitute values into the formula. SMILE has 5 letters, and we choose 5.

5P5 = 5! / (5 - 5)!

5P5 = 5! / 0!

Zero factorial (0!) is always 1.

So, 5P5 = 5! / 1

5! = 5 × 4 × 3 × 2 × 1

5! = 120

Therefore, 5P5 = 120 / 1, which is 120. We can arrange the word SMILE in 120 different ways.

User Shosti
by
2.8k points