Question

How many three letter words can be formed by using the letters of the word ${}^{\prime }EQUATIO{N}^{\prime }$ such that at least one vowel should be included in each word? (repetition of letters not allowed)

• A. $336$
• B. $6$
• C. $339$
• D. $330$

Answer 1

The correct option is D $330$

In the word EQUATION . There are $5$ distinct vowels.

1. With $1$ vowel , and $2$ consonant.

${}^5{c}_1{\times }^3{c}_2\times 3!=90$

2. With $2$ vowels and $1$ consonant.

$5c_2\times 3c_1\times 3!=180$

3. With all three vowels

$5c_3\times 3!=60$

Total $=330$