
### Instruction: help me answer this question How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?, think step by step
### Assistant: The word DAUGHTER has 3 vowels, A, E, U and 5 consonants D, G, H, T and R. The three vowels can be chosen in 3C2, as only two vowels are to be chosen. Similarly, the five consonants can be chosen in 5C3 ways. The number of choosing 2 vowels and 5 consonants would be 3C2 ×5C3. Each of these 5 letters can be arranged in 5 ways to form different words. , The answer is The total number of words formed would be = 30 × 120 = 3600
