Combinations, Permutation, & Probability Flashcards
What is the pigeonhole principle?
The idea that if you have k boxes & k+1 objects to be placed in the boxes, at least one box contains multiple objects
What is the generalized pigeonhole principle?
If N ≥ 0 are placed into k ≥ 1 boxes, at least one of the boxes has at least the ceiling of (N/k) objects
What is a permutation?
A distinct ordered sequence of elements
What is an r-permutation?
An arrangement of r elements out of n elements. P(n,r)
What is a combination?
A set of elements in which the order is not important. C(n, r), “n choose r”
What is the formula for a permutation?
n!/(n-r)!
What is the formula for a combination?
n!/((n-r)!r!)
What is the sum from k=0 to n of n choose k?
2^n
How can you find the coefficient of a term of a power of a binomial?
n choose k where n is the power of the binomial, & k is the power of x or y.
What is the formula for a combination if repetition is allowed?
C(n-1+r, r), where n is the number of items & r is the number you want
What is the key to the PIE?
Count how many time you add each section of the venn diagram or alternating sign
What does omega represent in probability?
The sample space, or the set of all possible outcomes of a random experiment
How do you calculate the probability of an event A?
|A|/| Ω |
What does P(B|A) mean?
The probability of B given A.
What is P(B ∩A) if they are dependent?
P(B|A)*P(A)
