If the permutation of $a, b, c, d, e$ taken all together be written down in alphabetical order as in dictionary and numbered, then the rank of the permutation $d e b a c$ is:

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Solution

The correct option is D 93
Rank of debac
$a . . . . = 4!$
$b . . . . = 4!$
$c . . . . = 4!$
$d a . . . = 3!$
$d b . . . = 3!$
$d c . . . = 3!$
$d e a . . = 2!$
$d e b a c = 1$
Rank $= 3 \times 4! + 3 \times 3! + 2! + 1$
$= 72 + 18 + 2 + 1$
$= 93$

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If the permutation of a,b,c,d,e taken all together be written down in alphabetical order as in dictionary and numbered, then the rank of the permutation debac is:

The correct option is D 93Rank of debaca....=4!b....=4!c....=4!da...=3!db...=3!dc...=3!dea..=2!debac=1Rank =3×4!+3×3!+2!+1=72+18+2+1=93

If the permutation of $a, b, c, d, e$ taken all together be written down in alphabetical order as in dictionary and numbered, then the rank of the permutation $d e b a c$ is:

The correct option is D 93
Rank of debac
$a . . . . = 4!$
$b . . . . = 4!$
$c . . . . = 4!$
$d a . . . = 3!$
$d b . . . = 3!$
$d c . . . = 3!$
$d e a . . = 2!$
$d e b a c = 1$
Rank $= 3 \times 4! + 3 \times 3! + 2! + 1$
$= 72 + 18 + 2 + 1$
$= 93$