combinatorics

[Adam1503]

Hello,

For several hours I have been trying to solve combinatorics problems and I have the last two items left.

I would very much like to ask for a solution or tips on what I should do.

1.4. A group of students consists of 12 men and 13 women. How many ways can there be
choose a representation of this group consisting of

(a) three men and four women, provided that two ladies: Anna and Barbara, no
want to be in the same representation (i.e. at most one of
them),

(b) three men and four women, provided there are two people: Adam and Anna, no
want to be in the same representation,

(c) three men and four women, provided that two people: Adam and Barbara,
they want to be in the representation at the same time or not to enter it at the same time.

Thank you in advance for your help.

One more thing - sorry if my English is incorrect - we don't have many forums.

 

[mikegonz00]

Little late to answer this, but I can give you some hints if you're still interested. Assign a number to each of the 12 men (1 through 12) and assign a number to each of the 13 women (1 through 13). Without loss of generality, for the women group, let label 1 go to Anna and label 2 go to Barbara.
(a) Sequence of two decisions (Product Principle): first choose a subset of size 3 of labels from the men group... then choose a subset of size 4 of labels from the women group. In how many of these cases do label 1 and label 2 appear together for the women? Difference Principle.
(b) Similar idea as (a)!
(c) Not sure if I understood what you're asking here, but you should probably be using the sum principle with two disjoint cases: (1) A and B together or (2) A and B not together. (2) is just like (b).

Side note: these hints assume that Adam is from the men group