1 .
Consider strings consisting of 12 characters, where each character is an element of the set $\{a,b,c,d,e\}$.
The positions in such strings are numbered as $1,2,3,\dots,12$.
How many such strings have the property that
How many such strings have the property that
- each even position contains an element of $\{a, b, c\}$, or
- each odd position contains an element of $\{d,e\}$?
(a)
$3^{6} \cdot 5^{6} + 2^{6} \cdot 5^{6}$
(b)
$6^{3} \cdot 6^{5} + 6^{2} \cdot 6^{5} - 6^{2} \cdot 6^{3}$
(c)
$3^{6} \cdot 5^{6} + 2^{5} \cdot 5^{6} - 2^{6} \cdot 3^{6}$
(d)
$6^{3} \cdot 6^{5} + 6^{2} \cdot 6^{5}$