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
$=210 times 120$
$=25200$
