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,
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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
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