Supplement: After reading Xinyu Stone's answer, I found that I was wrong.

But to add, her approach is also wrong.

The correct one should be: 4 * 3 * 2 *1-1* 2 *1*1* 4 * 3/2 *1= 9.

Explanation:

4*3*2* 1 is all cases;

4 * 1 *2 * 1 is the case that only 1 people have taken their own cards, that is, 1 (only 1 is the case that Party A has taken his own cards) *2 (Party B cannot take his own cards, but Party A has been taken away, only Party C and Party D.

2* 1 is a situation where only two people have their own cards. Once these two people take their own cards, the other two people will definitely not take theirs, so the result is C2/4;

1 is a situation where three people hold the cards themselves.