We have been given that Baby Kelsey wants to arrange 12 blocks in a row. In order to find the total number of different arrangements, we can use theorem of counting principle.
In the first position she has 12 options.
Now, one block is already in the first position hence now she has 11 options.
Similarly, at the third position she has 10 options.
Hence, using the counting principle, the number of different arrangements are
[tex]12\times 11\times 10\times 9\times 8\times 17\times 6\times 5\times 4\times 3\times 2\times 1\\
\\
=1163289600[/tex]
Therefore, 1163289600 different arrangements can she make.
