n!=n(n−1)(n−2)(n−3)....(3)(2)(1)

Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants can be found using the concept of permutations.

Given:
Number of vowels = 4
Number of consonants = 5

To form a word with 2 vowels and 3 consonants, we need to select 2 vowels out of 4 and 3 consonants out of 5. The order of selection matters because the arrangement of vowels and consonants will result in different words.

To find the number of ways to select 2 vowels out of 4, we can use the concept of combinations. The number of ways to select r items out of n is given by the formula:

nCr = n! / (r!(n-r)!)

where n! denotes factorial of n.

Using this formula, the number of ways to select 2 vowels out of 4 can be calculated as:

4C2 = 4! / (2!(4-2)!) = 4! / (2!2!) = (4*3*2!) / (2!*2!) = 6

Similarly, the number of ways to select 3 consonants out of 5 can be calculated as:

5C3 = 5! / (3!(5-3)!) = 5! / (3!2!) = (5*4*3!) / (3!*2!) = 10

Now, we need to find the total number of words formed by arranging these selected vowels and consonants. The order of arrangement matters, so we can use the concept of permutations.

The number of ways to arrange 2 vowels is given by:

2P2 = 2! = 2

Similarly, the number of ways to arrange 3 consonants is given by:

3P3 = 3! = 6

Therefore, the total number of words formed by 2 vowels and 3 consonants can be calculated as:

Total number of words = Number of ways to select vowels * Number of ways to select consonants * Number of ways to arrange vowels * Number of ways to arrange consonants

Total number of words = 6 * 10 * 2 * 6 = 720

Hence, the correct answer is option C) 7200.