Date: May 18, 2012 3:46 AM
Author: Mahesh
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.