Question

Out of $ 6 $ consonants and $ 3 $ vowels from the standard English alphabets, how many words or strings that consist of $ 2 $ consonants and $ 2 $ vowels(without repetition of any alphabet) can be formed?

• A. $ 1080 $
• B. $ 540 $
• C. $ 270 $
• D. $ 180 $

Answer 1

Answer: (A)

Number of ways of selecting (2 consonants out of 6) and (2 vowels out of 3)
$=^{6}C_{2} \times^{3}C_{2}=45$
Now, each word contains $4$ letters
Number of ways of arranging $4$ letters among themselves $= 4! = 24$
$\therefore $ Required number of words that can be formed
$=45\times 24=1080$