We are given 10 cards numbered - 1,1,2,2,3,3,4,4,5,5. Wherein card with same number are identical. We shuffled the card and kept them in two boxes. We kept the first 5 cards in box 1 and next 5 cards in box 2.
Now we have to find the number of ways in which we can draw the card from the boxes. Our procedure of drawing is picking 1 card each from each box. Just for clarification, we draw it like-
One card from box1
One card from box2
One card from box1
One card from box2
One card from box1
One card from box2
One card from box1
One card from box2
One card from box1
One card from box2.
I've made some progress in the question. There would be three cases of picking the card in the box.
Case 1- 2 pair of card are same in box 1 and box 2 together.
Case 2−1 pair of card is same in box 1 and box 2 together.
Case 3- all cards are different in both the box.
Number of ways of drawing card in each case is. Case1−(5!∗5!)/(2!∗2!)(2!∗2!), Case2−(5!∗5!)(2!∗2!), Case3−(5!∗5!).
But I'm not understanding how to go further and what to do with these. So I want the answer till the end of it. Plz help. I suppose that I will get an answer instead of suggestion.