i have to solve this problem but can you use pictures or symbols that will help alot

Question

Danny Connie and Jane have 8 cookies to share among themselves . They decide that each do not need to receive the same number of cookies, but each should receive at least one cookie. If the children do not break any of the cookies in how many different ways can they share the cookies ?

Answer 1

There are some interesting ways to think about this problem (depending on the level of math that you use).    For classes studying combinations and probabilities, there are formulas; for computer science classes, there are enumeration (list them all) techniques; for the beginning classes, there are pictures.

One of the most interesting ideas is that the number of cookies “counts” from 1 to 6 for each person (like a gas pump does, but the pump goes from 0 to 9 for units, then tens, then hundreds, then …).  The “constraint” (limitation) is that the sum of the 3 digits must equal 8 (that’s why the counter goes from at least 1 to no more than 6).  So, you could use a formula to determine how many or you could just list them all.

Well, here they are.  You don’t need a computer just to count them.  (But, do see how the "counter" works.  And, do check out how many ways there are for each of the values of the first digit!)

 

1   1   6

1   2   5

1   3   4

1   4   3

1   5   2

1   6   1

2   1   5

2   2   4

2   3   3

2   4   2

2   5   1

3   1   4

3   2   3

3   3   2

3   4   1

4   1   3

4   2   2

4   3   1

5   1   2

5   2   1

6   1   1