Anyone good with combinations/permutation

[baywatch123]

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So this is just a small manipulation of a question i did... i just wanted to see if i'm doing it right

Question: You are travelling to South America in two weeks. A friend bought you 5 watches and 6 pairs of sunglasses. You can bring at least 2 watches and at least 1 pair of sunglasses, and can only bring 4 items (so you don't lose all of them). How many combinations of watches and sunglasses can you have?


This is my thought process:
First, 5C2 (for the at least 2) = 10
Second, 6C2 (to fill remaining last 2 "spots") = 15
Multiply subsets = 150.

5C3 (since it was at least 2) = 10
6C1 (to fill in last spot) = 6
Multiply subset = 60

Add 150+60 = 210 possible combinations....

is this correct? is my thought process right. with the limit of "4 items" i feel like i didn't need to add "at least 1 pair of sunglasses"

what if the question instead stated, "you only want to bring 2 watches and 2 sunglasses...." then would it just be
5C2 = 10
6C2 = 15
and then multiply? to get 150 combinations?

thanks

 

[baywatch123]

bump/help

 

[cdp1210]

Yes you are right on all of this, you seem to have the hang of it. Always start the problem by breaking what the question is asking and all the possibilities.

So with this question, there are only 2 choices for what you can bring: either 3 watches/1 pair of sunglasses or 2 watches/2 pair of sunglasses.

So that equation would be: (5C3)(6C1)+(5C2)(6C2) = 210.

If the question was "you only want to bring 2 watches and 2 sunglasses....", then yes it would simply be (5C2)(6C2) = 150

 

[baywatch123]

ahhhh sweet thank you1!!!