A deck of playing cards is shuffled and arranged into thirte

A deck of playing cards is shuffled and arranged into thirteen piles each of which consists of 4 cards. Show that you can always select one card from each pile so that all of your selected cards have different ranks (i.e., you selected exactly one ace, one 2, one 3, etc.).

Solution

Total 52 cards

Heart (13) + Dimoand (13) + Spades (13) + Clucb (13)

Select one card from each pile so that all of your selected cards have different ranks

Therefor Probability of one card = favourable outcome / total no of outcome

= 1/13

but we have to select 4 cards each of them

so = 4/13

Answer