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,Â
the number of selecting 3 consonants and 2 vowels is
​\( =^7C_3 \times ^4C_2 \)​Â
​\( =\frac{7!}{3!4!} \times \frac{4!}{2!2!} \)​
​\( =\frac{7.6.5}{3.2.1} \times \frac{4.3}{2.1} \)​
​\( =35 \times 6 \)​
​\( =210 \)​
Now, the number of ways of arranging 5 letters among themselvesÂ
​\( =5! \)​
=120Â
​\( \therefore \)​ the total number of words of 3 consonants and 2 vowels
​\( =210 \times 120 \)​
​\( =25200 \)​