1 . Consider strings of length $83$, in which each character is one of the characters $a,b,c,d,e$. How many such strings have exactly $20$ letters $e$?
(a)
$\binom{83}{5}\cdot 4^{63}$
(b)
$\binom{83}{5}\cdot 5^{63}$
(c)
$5^{20}\cdot 4^{63}$
(d)
$\binom{83}{20}\cdot 5^{63}$
(e)
$\binom{83}{20}\cdot 4^{63}$