Question

In a well-shuffled ordinary 52-card deck, what is the probability that the ace of spades and the ace of clubs are adjacent to each other?

please don't copy from different websites. I have already looked at them but I did not get it. I need further explanation.

Answer 1

Number of ways to arrange 'n' cards in any order = n!

Number of ways to arrange 52 cards = 52!

Consider ace of spades and the ace of clubs as one card. Then total number of cards will become 51. Number of ways to arrange 51 cards = 51!

Now, ace of spades and the ace of clubs (2 cards) can be arranged in 2! ways.

Total number of ways to arrange when the ace of spades and the ace of clubs are adjacent to each other = 51! * 2!

Probability that the ace of spades and the ace of clubs are adjacent to each other

= Total number of ways to arrange when the ace of spades and the ace of clubs are adjacent to each other / Total number of ways to arrange 52 cards

= 51! * 2! / 52!

= 2/52

= 1/26