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?

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

Tardigrade Admin · Accepted Answer

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

∴

Required number of words that can be formed

= 45 \times 24 = 1080

Q. 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?

$1080$

$540$

$270$

$180$

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 $= 4! = 24$
$∴$ Required number of words that can be formed
$= 45 \times 24 = 1080$

Q. 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?

1080

540

270

180