Combination or Permutation... or something else?

Question

I have been having trouble with this problem, and I can't seem to find a definite answer on how to work it out.

Q. A rugby league team of 13 consists of five backs, six forwards and two halves. How many teams are possible from a squad of 17, consisting of six backs, eight forwards and two halves, and one player who could play as a back or a half?

Normally I would treat it as a combination, but I am unsure how to treat the last player which can play as either, because if he/she is chosen for one position, they are no longer there for selection for the second possible position. (So I can't double them up).

Answer 1

HINT

I would consider the following three possibilities:

1. The player that can double is picked as a back

2. The player that can double is picked as a half

3. The player that can double is not picked at all

Calculate the number of possibilities for each of those, and add them up.

Answer 2

Let's treat the player that can play back or half as the "flex player".

Now we have three cases to sum together:

1 The flex player is in the back position

2 The flex player is in the half position

3 The flex player is not selected

See if you can figure out how to find the number of teams for each case, then simply add them together for the total number of teams possible.