1 . Consider strings of length $78$, in which each character is one of the characters $a,b,c,d,e$. How many such strings have exactly $7$ letters $e$?
(a)
$\binom{78}{5}\cdot 4^{71}$
(b)
$\binom{78}{5}\cdot 5^{71}$
(c)
$\binom{78}{7}\cdot 5^{71}$
(d)
$5^{7}\cdot 4^{71}$
(e)
$\binom{78}{7}\cdot 4^{71}$