Answer:
There are 5! = 120 possible ways to order the five cards in the packet. To find the probability that the two aces end up side by side, we can count the number of ways in which the two aces are adjacent and divide by the total number of possible orderings.If we consider the two aces as a single unit, there are 4! = 24 ways to arrange the three-card unit {AA, 2S, 3D, 4C} with the aces together. However, the aces can be arranged within the unit in two ways (Ace of Spades - Ace of Hearts or Ace of Hearts - Ace of Spades). So there are 2 x 24 = 48 ways to arrange the five cards with the two aces together.Therefore, the probability that the two aces end up side by side is 48/120 = 2/5 or 0.4.: