How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

To find the number of words that can be formed from the letters of the word "INVOLUTE" with 3 vowels and 2 consonants, we can use the concept of permutations.

Step 1: Count the number of vowels and consonants in the word "INVOLUTE".

• There are 3 vowels: I, O, and U.
• There are 5 consonants: N, V, L, T, and E.

Step 2: Determine the number of ways to arrange the vowels.

• Since we need to choose 3 vowels, we can use the formula for permutations: nPr = n! / (n - r)!
• In this case, n = 3 (number of vowels) and r = 3 (number of vowels we need to choose).
• So, the number of ways to arrange the vowels is 3P3 = 3! / (3 - 3)! = 3! / 0! = 3! = 3 * 2 * 1 = 6.

Step 3: Determine the number of ways to arrange the consonants.

• Similarly, we need to choose 2 consonants out of 5.
• So, the number of ways to arrange the consonants is 5P2 = 5! / (5 - 2)! = 5! / 3! = 5 * 4 = 20.

Step 4: Multiply the number of ways to arrange the vowels and consonants.

• Since the arrangement of vowels and consonants is independent, we can multiply the number of ways to arrange them.
• So, the total number of words that can be formed is 6 * 20 = 120.

Therefore, there are 120 words, with or without meaning, that can be formed from the letters of the word "INVOLUTE" with 3 vowels and 2 consonants.