+
Related Flashcards
Cards In This Set
| Front | Back |
|
Almost all counting problems can be thought of in terms of
|
The number of spots that are available and the number of possibilities for each spot.
|
|
Permutations
|
Arrangement matters - the number of elements often corresponds to the number of available slots for these elements or where items cannot be reused
|
|
Combinations
|
Order does not matter - often corresponds to when a smaller group of elements is drawn from a larger pool
|
|
Zero factorial
|
Equals 1
|
|
When you are determining a permutaiton where the number of available items (N) equals the number of spots (K) in which to arrange those items the answer is
|
Simply N!
|
|
For all permutations where N does not equal K
|
The total number of permutations = N! / (N-K)!
|
|
If a question asks for the number of different arrangements of x elements, when those elements are arranged in a circle use the formula
|
(x-1)!
|
|
The number of arrangements of N elements where certain elements are repeated is represented by
|
N! / A!B! where N is the number of items being arranged and each factorial in the denominator represents an item that is repeated and the variable represents the number of times the items repeats ex: arranging the letters A, B and B so there are 3 items, N=3 and we have one item that repeats 2 tiems. Therefore, the answer 3!/2! = 3
|
|
If K is changing in a permutation problem
|
1) Look for trigger words like "At least", "At most", and "Or"2) If K is changing in the problem, sum up all the results for the different values of K given one value for N
|
|
Because rearranging the elements in questions where the order is irrelevant will not create a new combination
|
All combination problems deal with selecting a smaller subset from a larger pool
|
|
Equation for solving most combinations
|
The number of unordered arrangements consisting of K items selected from a pool of N elements: N! / K! * (N - K)!
|
|
Examples of a permutation
|
1) Letters in a password without repetition2) Arrangements of 5 students in 5 seats
|
|
Examples of a permutation with repeating elements
|
1) Arrangements of different vases, two of which are identical2) Arrangements of letters, some of which are repeated
|
|
Examples of a combination
|
1) Members or a committee or students in a study group
|
|
The entire spectrum of probabilities of any event falls between
|
0 and 1, inclusive
|
