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?
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
Well, with a Halloween makeup kit like that, the number of possible disguises is almost as infinite as my collection of clown shoes! Let's do some calculations, shall we?
Since you can choose to use or not use each item, we can use the formula for combinations to calculate the total number of possibilities.
First, let's find the total number of combinations for each item:
- For the moustaches, we have 3 choices (use 1, use 2, use 3)
- For the eyebrows, we have 2 choices (use 1, use 2)
- For the noses, we have 4 choices (use 1, use 2, use 3, use 4)
- For the ears, we have only 1 choice (use it)
To calculate the total number of disguises, we multiply the number of choices for each item:
3 (moustache choices) × 2 (eyebrow choices) × 4 (nose choices) × 1 (ear choice) = 24 disguises
So, you have a whopping 24 disguises waiting to be unleashed! That's enough to confuse your friends and family for days. Just make sure your clown makeup game is on point!
To determine the number of disguises using at least one of these items, we can use the concept of combinations.
Since each component (moustaches, eyebrows, noses, and ears) can be chosen independently, we need to find the total number of combinations for each component and then multiply them together.
For the moustaches, we have 3 different options (assuming at least one is used).
For the eyebrows, we have 2 different options (assuming at least one is used).
For the noses, we have 4 different options (assuming at least one is used).
For the ears, we have 1 set.
To calculate the total number of disguises, we multiply the number of options for each component:
Total disguises = Number of moustache options × Number of eyebrow options × Number of nose options × Number of ear sets
Total disguises = 3 × 2 × 4 × 1 = 24
Therefore, there are a total of 24 different disguises possible using at least one of the items in the Halloween makeup kit.
To calculate the number of disguises using at least one of the items in the Halloween makeup kit, we can use the principle of inclusion-exclusion.
First, let's calculate the total number of possible disguises without any restrictions. We can do this by multiplying the number of options for each item together:
Number of mustaches = 3
Number of sets of eyebrows = 2
Number of noses = 4
Number of ears = 1
Total number of disguises without restrictions = 3 x 2 x 4 x 1 = 24
Next, let's calculate the number of disguises that do not use any of the items. Since each item is optional, this means we can exclude it from the total count. Therefore, the number of disguises without using any of the items is simply 1 (since it includes no items).
Now, we can calculate the number of disguises using at least one of the items by subtracting the number of disguises without using any item from the total number of disguises without restrictions:
Number of disguises using at least one item = Total number of disguises without restrictions - Number of disguises without using any item
Number of disguises using at least one item = 24 - 1 = 23
So, there are 23 different disguises possible using at least one of the items in the Halloween makeup kit.