- #1
doktorwho
- 181
- 6
Homework Statement
Using the common logic and known combinatorics properties solve the following problems:
a) If you have 6 letters and 6 envelopes, each having it's corresponding envelope in how many ways can you place every letter in the wrong envelope? (1 letter goes into 1 envelope)
b)You have been given a set ##A={1,2...50}##. Determine the number of subsets of A that have 5 elements, which don't include 45 and which don't include two succesive numbers.
Homework Equations
3. The Attempt at a Solution [/B]
The first one should be relativly simple and i just wanted to check my result with you.
Lets say you have the first envelope. Number of wrong letters that you can put into it is 5 and so on for the every envelope and the result is ##5^6##. Do you agree?
The second one is what I am really curious about. I thought of it the similar way i did with the upper problem.
Lets say i want to create that subset. I have 5 empty places for the elements. I can't have 49 and that leaves me with 49 possibilities. For the second place i can have 48 possibilities because i can't have 49 and the successor of the one in the first place.
That leaves me with the result ##49*48^4##. What do you think?