# Math Help - Permutation-1

1. ## Permutation-1

If the permutations of a,b,c,d,e taken all together be written dowe in alphabetical order as in dictionary and numbered, find the rank of the permutation debac.

If the permutations of a,b,c,d,e taken all together be written dowe in alphabetical order as in dictionary and numbered, find the rank of the permutation debac.
The number of permutations that begin with a..., b... or c... is:
$3\times 4! =72$
The number that begin with da..., db..., dc... or dd... is
$4\times 3! = 24$
The number that begin with dea is
$1\times 2!=2$
And debac is the first one beginning with deb... So this is ranked number
$72 +24+2+1 = 99$