Let's break down the problem step-by-step.

Given Word:

The word is "DAUGHTER".

Identifying Vowels and Consonants:

• Vowels in "DAUGHTER": A, U, E (3 vowels)
• Consonants in "DAUGHTER": D, G, H, T, R (5 consonants)

Choosing the Letters:

1. Choose 2 vowels out of 3:
   The number of ways to select 2 vowels from 3 is given by the combination formula:

   $\binom{3}{2} = \frac{3!}{2!(3-2)!} = 3$

2. Choose 3 consonants out of 5:
   The number of ways to select 3 consonants from 5 is:

   $\binom{5}{3} = \frac{5!}{3!(5-3)!} = 10$

Forming the Words:

Each selection of 2 vowels and 3 consonants gives us a set of 5 distinct letters. The number of ways to arrange 5 distinct letters is:

$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

Calculating the Total Number of Words:

The total number of words formed is given by multiplying the number of ways to choose the vowels and consonants, and the number of permutations of the selected letters:

$\binom{3}{2} \times \binom{5}{3} \times 5! = 3 \times 10 \times 120 = 3600$

Thus, the total number of words that can be formed is:

$\boxed{3600}$

Would you like me to explain any specific step further, or have any questions?

Related Questions:

1. How many distinct permutations can be made from all the letters in "DAUGHTER"?
2. What is the number of words formed if 3 vowels and 2 consonants are chosen instead?
3. How many distinct 4-letter words can be formed from "DAUGHTER"?
4. What is the probability of randomly choosing a 5-letter word with at least 2 vowels from "DAUGHTER"?
5. If repetitions are allowed, how many 5-letter combinations can be made using "DAUGHTER"?

Tip: Always identify distinct groups (vowels and consonants) separately when dealing with letter arrangements in words.