In how many different ways can the letters of the word 'MATH' be arranged?
Practice Questions
1 question
Q1
In how many different ways can the letters of the word 'MATH' be arranged?
12
24
16
8
The word 'MATH' has 4 distinct letters. The number of arrangements is 4! = 24.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many different ways can the letters of the word 'MATH' be arranged?
Solution: The word 'MATH' has 4 distinct letters. The number of arrangements is 4! = 24.
Steps: 7
Step 1: Identify the letters in the word 'MATH'. The letters are M, A, T, and H.
Step 2: Count the number of letters. There are 4 letters in total.
Step 3: Understand that we can arrange these 4 letters in different ways.
Step 4: Use the factorial notation to find the number of arrangements. The notation for factorial is 'n!', where 'n' is the number of items to arrange.
Step 5: Calculate 4! (which means 4 factorial). This is done by multiplying 4 × 3 × 2 × 1.
Step 6: Perform the multiplication: 4 × 3 = 12, then 12 × 2 = 24, and finally 24 × 1 = 24.
Step 7: Conclude that there are 24 different ways to arrange the letters of the word 'MATH'.
