Question

There are n balls in a jar, labeled with the numbers 1, 2, . . . , n. A total of k balls are drawn, one by one with replacement, to obtain a sequence of numbers. What is the probability that the sequence obtained is strictly increasing? (e.g. {1, 2, 3, 5} is strictly increasing and {1, 2, 2, 5} is not)

Answer 1

Answer:

probability that the sequence obtained is strictly increasing = nCk/(n^k)

nCk are the ways we can choose k balls out of n balls.

Step-by-step explanation:

See attached picture.

Answer 2

Answer:

The probability that the sequence obtained is strictly increasing is; (nCk)/(n^(k))

Step-by-step explanation:

Every time a ball is drawn and put back in a jar and independent from each other, it will be observed that the number of possible outcomes is n^(k) ways.

Mow, if we pick a number of different balls from the jar. Let's call this number ''k". We can do it in C(n, k) ways.

If we sort them out in a row by their number, we will observe that the sequence is strictly increasing. Thus, we would have uniquely determined every strictly increasing sequence. Thus, the probability is;

(nCk)/(n^(k))