
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
September 27th, 2018, 08:03 AM  #1 
Newbie Joined: Sep 2018 From: India Posts: 2 Thanks: 0  Permutations and Combinations Problem
There are n number of chocolates. We can pick either 1 or 3 chocolates at once. In how many ways can we pick all the chocolates? The n variable can have any value as 30,100,50 etc. 
September 27th, 2018, 08:47 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,319 Thanks: 1023  
September 27th, 2018, 09:37 AM  #3 
Newbie Joined: Sep 2018 From: India Posts: 2 Thanks: 0 
If n=1: There can be one possible way. If n=2: There are two possible ways. One on the first pick, and another one on second. if n=3: There can be 4 combinations. Either all chocolates at once or one by one. I hope this gives an idea about the problem. 
September 27th, 2018, 10:33 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,404 Thanks: 1306 
The problem is given $n$ find $j, ~k \ni 3j + k = n$ fixing $j$ we see that $k = n  3j$ i.e. it is fixed for a given $j$ We also note that $0 \leq j \leq \left \lfloor \dfrac{n}{3} \right \rfloor$ So a given $n$ has $ \left \lfloor \dfrac{n}{3} \right \rfloor+1$ different combinations of 1's and 3's that sum to it. 

Tags 
combinations, permutations, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Does this problem fall into Combinations and Permutations easy question?  adambishopluv18  Probability and Statistics  1  October 21st, 2017 01:06 PM 
combinations and permutations  xiang1805  Advanced Statistics  3  March 16th, 2016 12:32 AM 
A problem regarding Permutations n Combinations  hello2413  Advanced Statistics  2  March 20th, 2010 09:36 AM 
Combinations/Permutations/multiplication problem  NeedHomeworkHelp  Algebra  1  March 2nd, 2010 05:42 PM 
A problem regarding Permutations n Combinations  hello2413  Number Theory  0  December 31st, 1969 04:00 PM 