Let X = {x1, x2,…, xn} and k be a positive integer with k ≤ n. Denote by

the ratio of the number of k-element permutations among the n elements without repetitions to the number of k-element permutations with repetitions.We also define

which is the corresponding ratio for combinations instead of permutations. What is the limit of the sequences pn and qn as n → ∞? Check if your results agree with the numerical evidence found in Exercise 11 of Section 2.7.

Transcribed Image Text:

Pn (n)k nk