Traditional Culture Encyclopedia - Travel guide - Six people are traveling and bringing 10 bottles of soda per day. Each person should bring at least one bottle. There are several ways to carry it.
Six people are traveling and bringing 10 bottles of soda per day. Each person should bring at least one bottle. There are several ways to carry it.
Solution: 126
Six people are traveling, each bottle contains 10 bottles of water.
First, let each person bring a bottle of water, and there are still 4 Bottles,
The key is how to arrange and combine the remaining four bottles.
The first situation:
There are four people bringing 2 bottles of water, then there are C(6,4)=15 ways.
Second case:
One person brought 3 bottles of water, and two people brought 1 bottle of water, then there is C(3,1)C(6,3)= 60 ways.
The third situation:
If two people bring 3 bottles of water, then there are C (6, 2) = 15 ways.
The fourth situation:
One person brought 4 bottles of water, and another person brought 2 bottles of water, then there is C(6,2)C(2,1)= 30 ways.
The fifth situation:
A person brings 5 ??bottles of water, then there are C (6, 1) = 6 ways.
To sum up, there are: 15+6315+6=126 methods.
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