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?
Answers
Reiny
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
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