Question

The number of words which can be formed with two different consonants and one vowel out of $7$ different consonants and $3$ different vowels, the vowel should be between the two consonants is

• A. 92
• B. 172
• C. 126
• D. 136

Answer 1

Answer: (C)

Selection of $2$ consonants from $7$ consonants $={ }^{7} C_{2}=21$
Selection of one vowel from $3$ different vowels $={ }^{3} C_{1}=3$
Now, we have $2$ consonants and a vowel and the vowel should be between consonants that is, cons. vow. cons.
$\therefore $ Two consonants can change their positions in $2 !$ ways.
Hence, by product rule, number of words
$=21 \times 3 \times 2=126$.