Assembling a robot from four part bins

Question

A build-your-own-robot kit has you pick exactly one part from each of four bins: 3 heads, 4 bodies, 3 arm-sets, and 2 wheel-sets. How many different robots can be assembled?

Accepted Answer

The four choices are independent, so by the multiplication principle we multiply the options in each bin: 3 	imes 4 	imes 3 	imes 2 = 72. Building up in stages confirms it: 3 heads times 4 bodies gives 12 partial robots, times 3 arm-sets gives 36, times 2 wheel-sets gives 72. Takeaway. The multiplication principle extends to any number of independent stages: just multiply them all. Four bins here give 3 	imes 4 	imes 3 	imes 2 = 72.

Assembling a robot from four part bins

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