how many ways to divide 3 sandwiches for 9 people
To find the number of ways to divide 3 sandwiches among 9 people, you can use the concept of combinations.
First, let's assume that all 3 sandwiches are identical, meaning they are the same type and size.
Now, think of this problem as distributing the 3 sandwiches among the 9 people using partitions. We can represent the people as 8 "dividers" since there are 9 people.
For example, if we arrange the dividers and sandwiches like this:
[] s [] s [] s [] s [] s [] s [] s [] s []
Each sandwich will be in one of the 9 sections between the dividers. The number of ways we can arrange the sandwiches can be found by selecting 2 out of the 8 positions for the sandwiches.
Thus, we need to find the number of combinations. The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
In this case, n = 8 (number of positions between the dividers) and r = 2 (number of sandwiches).
Using the formula:
C(8, 2) = 8! / (2!(8-2)!)
= 8! / (2! * 6!)
= (8 * 7) / (2 * 1)
= 28
Therefore, there are 28 different ways to divide 3 identical sandwiches among 9 people.
Does each person have to have an even piece?
In that case, you could cut each sandwich into 3 pieces and you would get 9 pieces. Do you understand?
Let me know how I can help you further?
All my best,
Dr. Anna