The letters of word 'postage' are to be arranged in the following manner:
(i) Vowels occupy even places.
(ii) Consonants are always together.
What will be number of words formed in (i) and (ii)?

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Solution

Letters $7, V 3 (a, e, o), C 4 (p, s, t, g)$
Total $= 7!$
(i) Three even places $2^{n d}, 4^{t h}$ and $6^{t h}$ in which 3 vowels can be fixed up in $3!$ ways and the remaining 4 consonants can be fixed up in $4!$ ways. Thus the total is
$3! . 4! = 6 \times 24 = 144$ .
(ii) Consonants together. Follow sting method.
Total number $= 4! . 4! = 576$

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The letters of word 'postage' are to be arranged in the following manner:(i) Vowels occupy even places.(ii) Consonants are always together. What will be number of words formed in (i) and (ii)?

Letters 7,V3(a,e,o),C4(p,s,t,g)Total =7!(i) Three even places 2nd,4th and 6th in which 3 vowels can be fixed up in 3! ways and the remaining 4 consonants can be fixed up in 4! ways. Thus the total is3!.4!=6×24=144.(ii) Consonants together. Follow sting method.Total number =4!.4!=576

The letters of word 'postage' are to be arranged in the following manner:
(i) Vowels occupy even places.
(ii) Consonants are always together.
What will be number of words formed in (i) and (ii)?