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The number of possible designs that are achievable are= 56.
The number of locations placed on the board,n = 8
The number of identical components, r = 5
The number of different designs that are possible can be calculated using the combination. This is because they are identical so the order in which they are selected does not matter.
The formula for combination =
[tex] \frac{n!}{(n-r)r!} [/tex]
That is
[tex] \frac{8!}{(8-5)5!} [/tex]
[tex] \frac{8×7×6×5!}{3×2×1×5!} [/tex]
[tex] \frac{8 \times 7 \times 6}{3 \times 2 \times 1} [/tex]
336/6 = 56
Therefore, the number of possible designs that are achievable are = 56
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