If each side of a cube can be either red or blue, how many distinct possibilities for a single cube are there in total?

2 for all R or all B

12 for one R or one B

30 for two R or two B

40 for three R or three B

30 for four R or four B

12 for five R or five B

= 105

Is there a better way to do this than to calculate the combinations with n!/r!(n-r)! for each number of altered colors?

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