Question

How many four letter words can be formed by using the letters of the word ${}^{\prime }EQUATIO{N}^{\prime }$ such that the atleast one vowel should be included in each word and also repetition of letters is not allowed?

• A. $1680$
• B. $3410$
• C. $1490$
• D. $2360$

Answer 1

Answer: (A)

$1680$

Given Word ,

$EQUATION$

Number of letters $=8$

Number of vowels $=5$

Number of consonants $=3$

There are only three consonants

In order to select four lettered word

Atleast one vowel should be selected

Every four lettered word from the the word EQATION has an vowel

Therefore number of words

${\Rightarrow }^8{P}_4\Rightarrow 8\times 7\times 6\times 5\Rightarrow 56\times 30\Rightarrow 1680$

Hence the correct answer is $1680$