Question

CSC 231 Discrete Structures and Its Applications. (DISCRETE MATHEMATICS) (ONLY ANSWER IF YOU KNOW DISCRETE STRUCTURES. PLEASE DON'T GUESS) (This is GENERALIZED PERMUTATIONS AND COMBINATIONS)

TO ANSWER THE QUESTION YOU HAVE TO FIRST FIGURE OUT IF IT'S 'r-permutations with repetition' or 'r-combinations with repetition'

1, How many PIN numbers of length 4 have at least one digit '9'? (hint: first find how many have a first digit '9', how many have a second digit '9',… then add it up.)

2. How many PIN numbers of length 4 have exactly one digit '9'? (hint: if the first digit is '9', how many choices remain for the second, third and fourth digit? Then think about if the second digit is ‘9’).

3. How many PIN numbers of length 4 either Start and End with '0' or have at least one digit '9'?

4.Show that if there are 30 students in a class, then at least two have last names that begin with the same letter. What is the name of the principle you can apply?

Answer 1

I HAVE EXPLAINED EACH OF THE 4 SOLUTION TO THE ABOVE MENTIONED 4 PROBLEMS BY WRITING ON A PAPER.

PLEASE READ IT CAREFULLY, EVERY POINT IS IMPORTANT AND IF U DO NOT UNDERSTAND ANY OF THE POINTS MENTIONED U CAN FEEL FREE TO COMMENT AND I WILL BE THERE TO HELP AS SOON AS POSSIBLE. I GAVE MY BEST EFFORT IN MAKING YOU UNDERSTAND.HOPE U WILL ENJOY THE SOLUTION.

THE PROBLEMS WERE BASED ON STANDARD MATHEMATICS OF PERMUTATION , COUNTING PRINCIPLE, PIGEONHOLE PRINCIPLE.SO PLEASE TRY TO UNDERSTAND IT IN AN EASY WAY AS MENTIONED.

AND PLEASE DO NOT FORGET TO GIVE A POSITIVE FEEDBACK IF YOU LIKE THE ANSWERS.

THANK YOU.

HERE ARE THE IMAGES.