Combinations And Permutations Flashcards
When the data points of a particular set are not all the same, what will the standard deviation not be equal to?
0
When is it a combination?
The order in which a task is completed does not matter
When is it a permutation?
The order in which a task is completed does matter.
What is the basic combination formula?
nCk = n! / (n-k)!k!
“N choose k”
Box & Fill Method:
Put a box for each decision. In each box put the # of players available for selection (should be lower with each decision). Then divide by the factorial of the total # of decisions.
If there are m ways to perform task 1 and n ways to perform task 2 and the tasks are independent, how many ways are there to perform both tasks together?
m * n
What are mutually exclusive events?
Events that cannot occur together
If there are x ways to accomplish event a and y ways to accomplish event b and if a and b are mutually exclusive, then how many ways are there to accomplish a OR b
x+y
“At least” means what?
And when you see “at least”, what does this usually mean?
= greater than or equal to
Typically involve addition of outcomes (or)
In combination problems, how do you solve when certain items MUST be selected.
Visualize as if the items that must be selected have already been selected. So your n (from n chose k) would be n-# that must be selected and your k would be k-# that must be selected
In combination problems, how do you solve when certain items MUST NOT be selected.
Visualize as if the items that must not be selected are excluded from the pool. So your n (from n chose k) would be n-# that must not be selected and your k would be unchanged.
What does it mean when two events are collectively exhaustive?
When two events are collectively exhaustive , the total # of ways in which the scenario can occur =
When the events represent all of the potential outcomes of the situation.
of ways in which a can occur + number of ways in which b can occur
What must you remember when calculating the number of ways in which at least one of x items must be chosen from y items?
Total # of ways to choose x items from y items - the number of way to choose none of the x items from y items = the number of ways to chose at least one of the x items from y
How do you solve dependent combinations?
The act of choosing the first combination limits the pool when choosing the subsequent combination
What is the easiest way to calculate an unknown number of items in a group?
Set up a box and fill diagram
What is the sum of all the numbers which can be formed by using n digits without repetition??
(n-1)!(sum of the digits)(111…n times)
