Arrangements of a standard deck of 52 playing cards if the denominations of the cards are ignored, so that only the suits are distinguished?I am struggling to see why my solution is wrong for this question.My solution:Number of arrangements of length k is 4 k and, since the maximum length is 52 we have that the total possible ways is 4 1 + … + 4 52 .

Name: Arrangements of a standard deck of 52 playing cards if the denominations of the cards are ignored, so that only the suits are distinguished?I am struggling to see why my solution is wrong for this question.My solution:Number of arrangements of length k is 4 k and, since the maximum length is 52 we have that the total possible ways is 4 1 + … + 4 52 .
Uploaded: 2022-02-23T17:22:57+00:00
Description: Arrangements of a standard deck of 52 playing cards if the denominations of the cards are ignored, so that only the suits are distinguished?I am struggling to see why my solution is wrong for this question.My solution:Number of arrangements of length k is 4 k and, since the maximum length is 52 we have that the total possible ways is 4 1 + … + 4 52 .

Question

Arrangements of a standard deck of 52 playing cards if the denominations of the cards are ignored, so that only the suits are distinguished?I am struggling to see why my solution is wrong for this question.My solution:Number of arrangements of length k is       4    k   and, since the maximum length is 52 we have that the total possible ways is       4    1    +  …  +      4          52      .

Belen Bentley · Accepted Answer

Step 1There are two problems with your answer. The first is you ignore the fact that there are exactly 13 of each suit. The number of arrangements of k cards is       4    k   for   k  ≤  13, but for   k  =  14 it counts arrangements with 14 of the same suit, so the correct answer is       4    k    −  4. The discrepancy grows as k gets larger. If you look for permutations of a multiset you can find information.Step 2The second is that the question requires you have all 52 cards in the arrangement, so you should not sum over k.