Question

How many arrangements of the letters of the word ${}^{\prime }BENGAL{I}^{\prime }$ can be made
i) If the vowels are never together
ii) If the vowels are to occupy only odd places

• A. $720,426$
• B. $4320,576$
• C. $822,593$
• D. $644,745$

Answer 1

The correct option is B $4320,576$

Given word BENGALI

Number of letters$=7$

Number of vowels $=3$

Number of consonants $=4$

(1) Total number of words $=7!$

Concider vowels to be one units

Integral arrangements $=3!$

Total number of uit $=6$

Arrangements $6!$

Required possiblities : $7!-6!$

$=6!(7-1)=6!\left(6\right)=4320$

Vowels occupy odd p;aces

${=}^9{P}_4\times 4!\times 3!=24\times 24=576$