10 pants, 29 shirts, 48 ties
How many different pants, shirts and ties outfits can you make?
Each outfit must have all 3 items
Answers
Answer:
Step-by-step explanations
Atleast 1pant 1shirt 1tie should be selected
10C1×29C1×48C1. (nC1=n)
10×29×48
=13920
Answer:
This is obviously a homework question, however I had a lot of problems with probability as well so I'd feel bad if I didn't help you. We can use two methods.
METHOD 1:(if you don't know permutations and combinations it would be better to look at method two)
We can use any two of the 9 (5 shirts + 4 pants) for a outfit so we can use 9C2, Let us put this in the equation.
9C2
Now there are also pairs where you are wearing two shirts or two pants (I'm assuming that won't be a pair lol) so we also have to subtract 5C2 (shirts) and 4C2(Pants), let us add these numbers in.
9C2–5C2–4C2 = 20
Now I won't add the math because you can do that yourself but the end result will be 20.
METHOD 2: (This is more simple however this can only be used on simpler problems)
In this method think of all the combinations and how to get them.
If there are 5 shirts and 4 pants, a pair can only be made by adding a shirt and a pant. So,
Shirt 1: Shirt 2: Shirt 3: Shirt 4: Shirt 5:
Pant 1. Pant 1 . . Pant 1. Pant 1. . Pant 1
Pant 2. Pant 2. . Pant 2. Pant 2. . Pant 2
Pant 3. Pant 3. . Pant 3. Pant 3. . Pant 3
Pant 4. Pant 4. . Pant 4. Pant 4. Pant 4
(Sorry if this model doesn't make sense)
Basically these are all the possible combinations if we distribute all the 4 pants to each shirt, so in short we multiply 5 * 4 to get 20.
ANSWER: 20