Multiple choice

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 ?

  1. $50000$
  2. $50100$
  3. $50300$
  4. $50400$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First, choose 2 different vowels from the 5 available, which can be done in 5C2 = 10 ways. Next, choose 2 different consonants from the 21 available, which can be done in 21C2 = 210 ways. Finally, arrange these 4 chosen letters to form a word in 4! = 24 ways, giving a total of 10 * 210 * 24 = 50,400 words.

AI explanation

First, select 2 different vowels from the 5 available using the combination formula 5C2, which equals 5 divided by 2 times 1, resulting in 10 ways. Next, select 2 different consonants from the 21 available using 21C2, which equals 21 times 20 divided by 2 times 1, resulting in 210 ways. For each selection of 4 letters, arrange them in a row using 4 factorial, which gives 24 different words. The total number of words is 10 times 210 times 24, which equals 50400.

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