Six couples are invited to play a game of cards, which needs 4 players

Six couples but no couple can play card game at a time. i.e. only a single person form each couple pair
Also, only 4 players can play the game at a time.

Step 1
We start with selecting 4 couples out of 6 couples. (Because only 4 players can play at one time.)

This is done in \(6C4\) ways. ===> \(6C4 = 6!/(4!*2!) \) = 15 ways.

Step 2
Now that we have selected the 4 couples, we select one from the pair who actually plays the card game.
(Because no couple should be included i.e. only one person from a couple pair can be selected)

4 couples, we can select 1 person from each pair. i.e. 2 choices per couple.
This is done is \(2^4\) = \(2*2*2*2\) = 16 ways.

Both conditions need to be satisfied, so it's an AND case of combination.
Total ways = 15*16 = 240 ways.

Answer C.