Question

A poker deck has 13 kinds (2s, 3s, ... , Kings, Aces) and 4 suits (Spades, Hearts, Clubs, Diamonds). Leave Factorials and products in the answers.

1. In how many ways can the cards be ordered if

a) Four Aces, in any order come first, then four kinds, in any order come second, ect.?

b) Four Aces, in any order, stay together, and the Four Kings, in any order, stay together, ect.? Briefly explain in a sentence or two. [So kings could come before the aces]

Now suppose all the 52 cards are ordered in List A and List B, where either list can be empty.

c) In how many ways can the cards be ordered in List A and List B if the Four Aces, in any order, are together on one list, and the Four Kings, in any order, are together on one list, ect. and on each list the kinds go from highest to lowest? Briefly explain in a few sentences.

d) How many ordered hands of five cards are possible if there are no two cards of one kind? Briefly explain.

Answer 1