$9\mathrm{.}2\mathrm{.}3$: Efficient trees for prefix codes.

Consider the following tree for a prefix code.

A text file contains only characters from the set $\{a,b,c,d,e,f\}.$ The frequency of each letter in the file is:

a: $5\%$

b: $5\%$

c: $10\%$

d: $15\%$

e: $25\%$

f: $40\%$

$($b$)$ Is there a prefix tree for the set $\{a,b,c,d,e,f\}$ that would result in fewer bits per character on average for the given frequencies of the characters?