Question

9 How many different arrangements of the letters of the word 'BENGAL'
can be done so thatxa) two vowels come together (b) two vowels do not come
together,
​

Answer 1

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!(6)

=4320

Vowels occupy odd p;aces

=

9

P

4

×4!×3!

=24×24

=576