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 1We 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 2Now 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.
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