Question

A printed circuit board has eight different locations in which a component can be placed. If five identical components are to be placed on the board, how many possible designs are possible

Answer 1

The number of possible designs that are achievable are= 56.

Calculation using combination

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 =

$\frac{n!}{(n-r)r!}$

That is

$\frac{8!}{(8-5)5!}$

$\frac{8×7×6×5!}{3×2×1×5!}$

$\frac{8 \times 7 \times 6}{3 \times 2 \times 1}$

336/6 = 56

Therefore, the number of possible designs that are achievable are = 56

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