Question

The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet ?

• A. $50000$
• B. $50100$
  
• C. $50300$
• D. $50400$

Answer 1

The correct option is D $50400$

$2$ vowels can be chosen in $5c_2$ ways.

$2$ consonants can be chosen in $21c_2$ ways.

$4$ letter can be arranged in $4$ ways.

$\therefore$ The no of words containing $2$ vowels and $2$ consonants $=5c_2\times 21c_2\times 4!=10\times 210\times 24=50400$