How to calculate the probability of a number appearing K times on a segment N?

Question

Mathematics

The random number generator generates N numbers from A to B. How to count the number of possible occurrences of the number n exactly K times?
For example:
10 numbers are generated from 1 to 5. Total possible variations of the number series: 5^10 = 9765625.
How many of these 9765625 ones will be generated exactly 4 times?

Answer 1

(number of ways to select k elements from n)*(number of ways to fill in nk elements)
for the first see "combinations", 2 you already know how to count.

Answer 2

C ₁₀ ⁴ ·(5−1) ¹⁰⁻⁴
Arrange ones (C ₁₀ ⁴ ) ways, then put everything else ((5−1) ¹⁰⁻⁴ ).
To calculate the probability, we must also divide by 5 ¹⁰