Question

if the permutations 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??????

Answer 1

Write down the first 20 or so entries in this alphabetical list and you'll begin to get a good sense of what is going on here.

Answer 2

abcde
abced
abdce
abdec
abecd
abedc
acbde
acbed
acdbe
acdeb
...

Answer 3

So then you need to know how to count up entries.
# of entries starting in a, b and c = ____
then the # entries starting with da, db and dc = ____
then # entries starting with dea = ____
....

Answer 4

it is a five digit number
so 1st place (int the place of d ) .....we have a,b,c so 3*4!
now when d is in 1st place then 2nd place may have a,b,c, means 1*3*3!
when b is at 3rd place means ....at third place bac has 3rd position if we permute a,b,c
so it might be 72+18+3=93