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You are given a set of blocks to build a panel using 3”×1” and 4.5”×1" blocks. For structural integrity, the spaces between the blocks must not line up in adjacent rows. There are 2 ways in which to build a 7.5”×1” panel, 2 ways to build a 7.5”×2” panel, 4 ways to build a 12”×3” panel, and 7958 ways to build a 27”×5” panel. How many different ways are there to build a 48”×10” panel? This is what I understand so far: with the blocks 3 x 1 and 4.5 x 1 I've used combination formula to find all possible combinations that the 2 blocks can be arranged in a panel of this size C = choose --> C(n, k) = n!/r!(n-r)! combination of group n at r at a time Panel: 7.5 x 1 = 2 ways --> 1 (3 x 1 block) and 1 (4.5 x 1 block) --> Only 2 blocks are used--> 2 C 1 = 2 ways Panel: 7.5 x 2 = 2 ways I used combination here as well 1(3 x 1 block) and 1 (4.5 x 1 block) --> 2 C 1 = 2 ways Panel: 12 x 3 panel = 2 ways --> 2(4.5 x 1 block) and 1(3 x 1 block) --> 3 C 1 = 3 ways 0(4.5 x 1 block) and 4(3 x 1 block) --> 4 C 0 = 1 way 3 ways + 1 way = 4 ways (This is where I get confused) Panel 27 x 5 panel = 7958 ways 6(4.5 x 1 block) and 0(3 x 1) --> 6 C 0 = 1 way 4(4.5 x 1 block) and 3(3 x 1 block) --> 7 C 3 = 35 ways 2(4.5 x 1 block) and 6(3 x 1 block) --> 8 C 2 = 28 ways 0(4.5 x 1 block) and 9(3 x 1 block) --> 9 C 0 = 1 way 1 way + 35 ways + 28 ways + 1 way = 65 ways As you can see here the number of ways is nowhere near 7958. What am I doing wrong here? Also h

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