Suppose I have a bundle of crayons, I have 5 different colours of crayon (Blue, Black, Brown, Red, Grey) how many unique bags can I create with 10 items per bag such that each bag has at least one of each crayon in each bag.
Now my question is can one use permutations and/or combinations…
If that is the case then is it an independent or dependent? Also how does one know when to use permutations and when to use combinations?
EDIT:
So this is how I went about doing it:
10 C 5 = 10!/(10-5)! 5!
=(10*9*8*7*6)/(5*4*3*2*1)
= 252
Would this be the correct way of going about doing this question?
Best Answer
Permutation can be thought of number of ways to order "something", while Combination is the number of ways of selecting "something".
Permutation = Selecting + Ordering.
Thinking along these lines has helped me reduce confusion in many PnC problems. I always tackle problems by selecting the items and than ask "Does the order matter?" If the answer is "Yes", permuate the answer by multiplying with apt factorial. If "No", you've arrived at the answer you needed.
Example: Let us assume there are 10 people waiting on a bus stop. Now a vehicle comes and there is space of 4 people on it. So the number of ways 4 people can get on the vehicle is 10 C 4, whereas the number of ways they can be seated is 10 P 4.
I hope this helps in visualization of further problems. As for this particular problem, Brian has explained it adequately.