How many 2-letter words can be made from the letters MATH if

repetition of letters is allowed?

repetition of letters is not allowed?

### 1. Repetition of letters is allowed:
When repetition is allowed, each letter in the 2-letter word can be any of the 4 letters in "MATH". So, for each of the two positions in the word, there are 4 possible choices.

The total number of 2-letter words is:

\[
4 \times 4 = 16
\]

### 2. Repetition of letters is not allowed:
When repetition is not allowed, the first letter can be any of the 4 letters in "MATH", but for the second letter, only 3 letters remain.

The total number of 2-letter words is:

\[
4 \times 3 = 12
\]

### Summary:
- **With repetition allowed:** 16 words
- **Without repetition allowed:** 12 words

Would you like any further details on this, or do you have any questions?

Here are some related questions:
1. How many 3-letter words can be made from "MATH" with and without repetition?
2. What is the number of 4-letter words that can be made with repetition allowed?
3. How many 2-letter words can be made from a 5-letter set like "MATHS" with and without repetition?
4. How would the result change if there were 5 positions instead of 2?
5. What if the set of letters contained a repeated letter, like "MATT"?

**Tip:** When repetition is allowed, the number of combinations for each position stays constant, while without repetition, the choices decrease after each selection.

How many 2-letter words can be made from the letters MATH if repetition of letters is allowed? Repetition of letters is not allowed?

Learn how to calculate the number of 2-letter words that can be made from the letters MATH, with and without repetition. This problem covers key combinatorics concepts such as counting with repetition and permutations without repetition. Suitable for students in Grades 6-8.

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