## Weekend combinatorics

5 Nov, 2022 at 13:58 | Posted in Varia | 6 Comments

Thinking of spending an extended weekend at his summer residence, yours truly wanted to take five of his favourite books with him. On my bookshelf are five books by Strindberg and four by Shakespeare. I thought of bringing with me at least two of the Strindberg volumes. In how many ways can I do this?

1. As usual Prof. Syll and rsm have difficulties with books and get the wrong answers.
Perhaps they should both try zero books and relaxation instead.
.
The question asked is:
“In how many WAYS” can Prof. Syll “BRING” the 5 volumes?
The question answered by Prof. Syll and rsm is merely:
“In how many COMBINATIONS” can the 5 volumes be ARRANGED”?
Plainly there are many more WAYS of BRINGING than merely 121 COMBINATIONS.
.
– There are 5! =120 different ways of ordering (permutations of) the volumes in each combination
ie 120 x 121= 14,520 permutations of volumes.
.
– There are 6 possible ways of placing each volume: face up, face down, standing vertically with top up, standing vertically with top down, standing spine down, standing spine up.
So there are 6! = 720 permutations of placements for each permutation of volumes.
.
– There are 359 possible degrees of orientation from North for each placement permutation.
So there are 359! = 1.10643525614411407728 e763
permutations of orientations for each permutation of placements.
.
And there are maybe 20 or more possible modes (or combined modes) of transport for each permutations of orientations.
etc

• May I thank you for showing that any math problem is really just an exercise in mindreading?

2. 106?

• Close, but no 🙂

• 121?

• You passed the test. Congrats!

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