How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Question:
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Solution:
2 out of 5 vowels and 3 out of 17 consonants can be chosen in ${ }^{5} C_{2} \times{ }^{17} C_{3}$ ways.
Thus, there are ${ }^{5} C_{2} \times{ }^{17} C_{3}$ groups, each containing 2 vowels and 3 consonants.
Each group contains 5 letters, which can be arranged in $5 !$ ways.
$\therefore$ Required number of words $=\left({ }^{5} C_{2} \times{ }^{17} C_{3}\right) 5 !=6800 \times 120=816000$