The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two…
The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?
$2100 \times 2 !$
$210 \times 2 !$
$210 \times 4 !$
$2100 \times 4 !$
Solution
Selection of two vowels $\Rightarrow{ }^5 \mathrm{C}_2$
Selection of two consonants $\Rightarrow{ }^{21} C_2$
Arrangements of four letters $\Rightarrow 4$ !
$\therefore$ Total words $={ }^5 C_2 \times{ }^{21} C_2 \times 4 !=2100 \times 4 !$