**Permutations with Repetition example question**

How many ways are there to assign three jobs to five employees if each employee can be given more than one job?

Solution to this **Discrete Math** practice problem is given in the video below!

**Combinations with Repetition example problem**

How many ways are there to select three unordered elements from a set with five elements when repetition is allowed?

Solution to this **Discrete Math** practice problem is given in the video below!

**Combinations with Repetition example**

A book publisher has 3,000 copies of a discrete mathematics book. How many ways are there to store these books in their three warehouses if the copies of the book are indistinguishable?

Solution to this **Discrete Math** practice problem is given in the video below!

**Combinations with Repetition HARD example question**

How many positive integers less than 1,000,000 have the sum of their digits equal to 19?

Solution to this **Discrete Math** practice problem is given in the video below!

**Combinations with Repetition HARD example problem**

How many solutions are there to the equation *x*_{1} + *x*_{2} + *x*_{3} + *x*_{4} + *x*_{5} = 21, where *x _{i }*,

*i*= 1, 2, 3, 4, 5, is a nonnegative integer such that

a)

*x*

_{1}≥ 1 ?

b)

*x*≥ 2 for

_{i}*i*= 1, 2, 3, 4, 5 ?

c) 0 ≤

*x*

_{1}≤ 10 ?

d) 0 ≤

*x*

_{1}≤ 3, 1 ≤

*x*

_{2}< 4, and

*x*

_{3}≥ 15 ?

Solution to this **Discrete Math** practice problem is given in the video below!

**Combinations with Repetition HARD example**

There are 10 questions on a discrete mathematics final exam. How many ways are there to assign scores to the problems if the sum of the scores is 100 and each questions is worth at least 5 points?

Solution to this **Discrete Math** practice problem is given in the video below!

**Distinguishable Objects & Distinguishable Boxes example question**

How many ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box?

Solution to this **Discrete Math** practice problem is given in the video below!

So many decent and nice problems to work, thank you so much

You rock, thank you for helping me before my exam