Question

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The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is

Answer 1

Here is an example for your question:-

Q) How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?

A.

16C7×7!


B.

12C4×4C3×7!

C.

12C3×4C4

D.

12C4×4C3

Solution:

4 consonants out of 12 can be selected in 12C4 ways.

3 vowels can be selected in 4C3 ways.

Therefore, total number of groups each containing 4 consonants and 3 vowels =12C4×4C3

Each group contains 7 letters, which can be arranging in 7! ways.

Therefore required number of words =12C4×4C3×7!

Answer 2

Answer:

(C) ------> 4950 × 7!

Step-by-step explanation:

Out of 12 consonant and 5 vowels, we have to choose 4 consonants and 3 vowels and arrange them among themselves.

Number of words = ¹²C × 5C

⁴ ³

= 12×11×10×9 x 5×4×3 x 7!

4×3×2×1 3×2×1

= 495 × 10 × 7!

= 4950 × 7!

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