Multiple choice

How many words can be formed with $2$ vowels and $3$ consonants from $5$ vowels and $6$ consonants?

  1. $^5C_2 \times 5!$
  2. $^5C_2 \times ^6C_3 \times 5! $
  3. $^5C_2 \times ^6C_3$
  4. $^6C_3 \times 5!$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To form a word with 2 vowels and 3 consonants, first select them: 5C2 ways for vowels and 6C3 ways for consonants. Then, arrange the 5 selected letters in 5! ways. The total is 5C2 * 6C3 * 5!.

AI explanation

To form the word, we must first select the letters and then arrange them. We choose 2 vowels out of 5 using 5C2, and we choose 3 consonants out of 6 using 6C3. Since the formed word has 5 letters, these letters can be arranged among themselves in 5 factorial ways. The total number of words is found by multiplying these independent choices, giving 5C2 multiplied by 6C3 multiplied by 5!.

Keep practicing — related questions