- #1
baywatch123
- 6
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Question: You are traveling 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?
thank you
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?
thank you