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Generalized Permutations & Combinations problems – Discrete Math & Combinatorics

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 x1 + x2 + x3 + x4 + x5 = 21, where xi , i = 1, 2, 3, 4, 5, is a nonnegative integer such that
a) x1 ≥ 1 ?
b) xi ≥ 2 for i = 1, 2, 3, 4, 5 ?
c) 0 ≤ x1 ≤ 10 ?
d) 0 ≤ x1 ≤ 3, 1 ≤ x2 < 4, and x3 ≥ 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!



 

 




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