Counting

Concepts

• Permutations and combinations from Probability and statistics 10 exercisesA permutation P(n,k) is an ordered arrangement of k elements from a set of n; a combination binom nk is a selection in which orde…
• Multiplication principle 10 exercisesIf a task is done in successive steps and step i admits n_i options regardless of how the earlier steps were done, the total numb…
• Factorial 10 exercisesThe factorial of an integer n≥ 0, written n!, is the product of the positive integers less than or equal to n; that of zero is on…
• Permutations with repetition 10 exercisesThe permutations with repetition of n objects, of which n_i are indistinguishable of a single type i (i=1,dots,k), are their dist…
• Pigeonhole principle 10 exercisesIf n objects are placed in k boxes, some box holds at least lceil n/krceil objects, and in particular two when n>k.
• Binomial coefficient 10 exercisesThe binomial coefficient binomnk, for integers 0≤ k≤ n, is the number of k-element subsets of a set with n elements.
• Binomial theorem 10 exercisesThe binomial theorem expresses the power (x+y)^n, with n a nonnegative integer, as a sum of terms whose coefficients are the bino…
• Combinations with repetition 10 exercisesA combination with repetition of size k from n types of object is an unordered selection of k objects in which each type may be c…