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Topic: Permutation problems
Replies: 13   Last Post: Aug 12, 2013 2:23 PM

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Ben Brink

Posts: 201
From: Rosenberg, TX
Registered: 11/11/06
RE: Permutation problems
Posted: May 18, 2012 8:48 AM
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Will check on your details later. But assuming you have correct answers to A through C, you may be able to use the pigeonhole principle: n(A u B u C) = n(A) + n(B) + n(C) - n(A n B) - n(A n C) - n(B n C) + n(A n B n C), where "u" denotes "union" and "n" denotes "intersection." But first check over your work on A, B and C. Thanks and will try to look at this later; it's a great problem!

> Date: Fri, 18 May 2012 03:46:00 -0400
> From:
> To:
> Subject: Permutation problems
> Q1. How many permutations are there of the 26 letters of the english alphabet that do not contain any of the strings fish,rat or bird?
> I was able to solve it partially.
> A: Permutations that do not contain fish
> B: Permutations that do not contain rat
> C: Permutations that do not contain bird
> |A|=26!-23! (i found 23! permutations that contain fish)
> |B|=26!-24!
> |C|=26!-23!
> Stuck at this point. Could not find intersection of A,B,C
> Q2. How many permutations of 10 digits either begin with the three digits 987,contain the digits 45 in the fifth and sixth positions or end with the three digits 123.
> A: Begin with 3 digits 987, containd 45 in the fifth and sixth positions
> B: End with 3 digits 123
> |A|=3!*5!*2!=1440
> |B|=3!*7!=30240
> |A intersection B|=3!*3!*2!=72
> |A union B|=30888. I get this answer but this isn't correct. Please find the error.
> Thank You.

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