Question:
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
A. 25200 B. 21300
C. 24400 D. 210
Answer:
3 consonants can be selected from 7 consonants in \( ^7C_3 \) ways.
2 vowels can be selected from 4 vowels in \( ^4C_2 \) ways.
\( \therefore \) by multiplication principle,
the number of selecting 3 consonants and 2 vowels is
\( =^7C_3 \times ^4C_2 \)
\( =\frac{7!}{3!4!} \times \frac{4!}{2!2!} \)
\( =\frac{7.6.5}{3.2.1} \times \frac{4.3}{2.1} \)
\( =35 \times 6 \)
\( =210 \)
Now, the number of ways of arranging 5 letters among themselves
\( =5! \)
=120
\( \therefore \) the total number of words of 3 consonants and 2 vowels
\( =210 \times 120 \)
\( =25200 \)
