11. (10 points) Above are the building blocks with one star, two stars, and three stars as shown in figures $(a)$, $(b)$, and $(c)$. There are 5 blocks with one star, 2 blocks with two stars, and 1 block with three stars. If several of these blocks are used to form a strip of five stars, how many different ways can this be done? (Figure $(d)$ is one of the possible arrangements).
【Analysis】Through analysis, we can know: There are several cases as follows
(1) $5=1+2+2$, this type involves choosing one from 3, (2) $5=1+1+1+1+1$, this type has only 1 way; (3) $5=2+3$, this type involves choosing one from 2,
(4) $5=3+1+1$, this type involves choosing one from 3; (5) $5=2+1+1+1$, this type involves choosing one from 4; Add these several cases together,

Solve accordingly.
【Solution】(1) $5=1+2+2$, this type involves choosing one from 3, there are $C_{3}{ }^{1}=3$ ways;
(2) $5=1+1+1+1+1$, this type has only 1 way;
(3) $5=2+3$, this type involves choosing one from 2, there are $C_{2}{ }^{1}=2$ ways
(4) $5=3+1+1$, this type involves choosing one from 3, there are $C_{3}{ }^{1}=3$ ways;
(5) $5=2+1+1+1$, this type involves choosing one from 4, there are $C_{4}{ }^{1}=4$ ways;

In total: $3+1+2+3+4=13$ ways
Answer: There are a total of 13 different ways to arrange.