In how many ways can Candice share $13$ KitKats and $14$ Twixes with her younger brothers? I'm trying to solve the following problem:

After a round of "trick or treating", Candice has 13 Kit Kats and 14 Twixes in her pillow case. Her mother asks her to share some (but not necessarily all) of the loot with her three younger brothers.
(A) How many different ways can she do this?
(B) How many different ways can she do this if she gives at least one of each type of bar to each of her brothers?

I have taken two approaches to part A, neither of which have been successful. Firstly I considered there being 13 stars, 14 circles and 3 bars and solving for 30C3.  Then I considered doing 16C3 + 17C3 but this didn't work either.  The second bit completely stumps me as I'm unable to solve the first part correctly.
Thank you.
 A: 
In how many ways can Candice share $13$ KitKats and $14$ Twix with her three younger brothers?

Candice can distribute the KitKats and Twix separately.  
Let $x_1, x_2, x_3$ be the number of KitKats she gives to each of her younger brothers; let $x_4$ be the number of KitKats she keeps for herself.  Then the number of ways she can share the KitKats with her younger brothers is the number of solutions of the equation
$$x_1 + x_2 + x_3 + x_4 = 13$$
in the nonnegative integers.

 As you evidently know, the number of solutions of the equation $$x_1 + x_2 + x_3 + x_4 = 13$$ in the nonnegative integers is $$\binom{13 + 4 - 1}{4 - 1} = \binom{16}{3}$$ since a particular solution corresponds to the placement of $4 - 1 = 3$ addition signs in a row of $13$ ones, and we must choose which $3$ of the $13 + 4 - 1 = 16$ positions required for $13$ ones and $3$ addition signs will be filled with addition signs.

Let $y_1, y_2, y_3$ be the number of Twix she gives to each of her younger brothers; let $y_4$ be the number of Twix she keeps for herself.  Then the number of ways she can share the Twix with her younger brothers is the number of solutions of the equation
$$y_1 + y_2 + y_3 + y_4 = 14$$
in the nonnegative integers.

 As you evidently know, the number of solutions of the equation $$y_1 + y_2 + y_3 + y_4 = 14$$ in the nonnegative integers is $$\binom{14 + 4 - 1}{4 - 1} = \binom{17}{3}$$

Since these choices are independent, we must multiply the number of ways Candice can distribute the Twix by the number of ways she can distribute the KitKats.

 This yields the answer $$\binom{16}{3}\binom{17}{3}$$

Of course, her mother may not be happy if Candice keeps all the KitKats and all the Twix for herself, a situation not ruled out in my calculations.

In how many ways can Candice share $13$ KitKats and $14$ Twix with her three younger brothers.

Strategy
She can begin by giving each of her brothers a KitKat and a Twix.  Then she will be left with $10$ KitKats and $11$ Twix to distribute among herself and her brothers.  
Can you take it from here?
