Out of 5 consonants and 4 vowels, how many words of 3 consonants and 2 vowels…

Step-by-Step Solution

To form words with a specific number of consonants and vowels, we must first select the required letters and then arrange them.

1. Select the letters:

   • Number of consonants to select = 3 out of 5. Ways to select = 5C3 = (5 × 4 × 3) / (3 × 2 × 1) = 10 ways.

   • Number of vowels to select = 2 out of 4. Ways to select = 4C2 = (4 × 3) / (2 × 1) = 6 ways.

   • Total ways to select the letters = 10 × 6 = 60 ways.

2. Arrange the selected letters:

   • Total number of letters selected = 3 consonants + 2 vowels = 5 letters.

   • These 5 letters can be arranged among themselves in 5! (5 factorial) ways.

   • 5! = 5 × 4 × 3 × 2 × 1 = 120 ways.

3. Calculate total words:

   • Total words = (Ways to select) × (Ways to arrange)

   • Total words = 60 × 120 = 7,200.