Question

a halloween makeup kit contain 3 different moustaches, 2 different sets of eyebrows,4 different noses, and a set of ears. (It is not nescessary to use any moustaches, ect..)How many disguises using at least one of these items are possible?

Answer 1

The three mustaches can be used in 4 different ways, that is
we could use any of the 3 of them
or we could none at all
in the same way the eyebrows can be used in 3 ways,
the noses in 5 ways, and
the set of ears in 2 ways.

so the number of different makeups is
4x3x5x2 = 120
but that includes taking none of the available items and that would not include a disguise.

so number of disguises is 120 - 1 = 119