Permutations and Combinations Problem

  • Thread starter Appleton
  • Start date
  • #1
91
0

Homework Statement


In how many ways is it possible to select one or more letters from those in INSIPIDITY?


Homework Equations





The Attempt at a Solution


My initial impression was that this was a combinations problem and I did not have to take into account the repetitions. This led me to over-count because I had counted combinations like SIPI multiple times as SI2PI3 and SI1PI4 are indistinguishable. The only method I could think of was for each number of selected letters to add up the mutually exclusive scenarios that constituted it, as follows

1 letter selected: no I involved, 1 I involved
2 letters selected: no I's involved, 1 I involved, 2 I's involved
3 letters selected: no I's involved, 1 I involved, 2 I's involved, 3 I's involved etc.

Apparently ((4+1)(1+1)^6) -1 is a much quicker solution, however I am unable to interpret the logic of this solution. Could someone please explain it to me? Also if anyone could offer some tips on how to tackle these problems I would appreciate it, I have found this to be the most difficult subject I have encountered so far, mainly because there doesn't seem to be a procedure to follow like there was for calculus.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
34,493
10,619
You can take (0, 1, 2, 3 or 4) letters "I" -> 4+1 options
You can take (0 or 1) letters "N" -> ...
...
All those choices are independent of each other.

mainly because there doesn't seem to be a procedure to follow like there was for calculus.
There are always many ways to find a solution, the more ways you know and recognize (needs practice!) the easier it is to find a good one.
 
  • Like
Likes 1 person
  • #3
91
0
Thanks for the help.
 

Related Threads on Permutations and Combinations Problem

Replies
2
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
6
Views
17K
  • Last Post
Replies
5
Views
6K
Replies
3
Views
828
Replies
1
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
6
Views
1K
Top