Question

Hi, I need help on my assignment for my discrete structures class. Thank you, and I will remember to rate your answer!

5. Consider the set of 3-digit integers between 100 and 999 inclusive. a. How many are divisible by 5? b. How many are divisible by 4? C. How many are not divisible by 5? d. How many are divisible by 4 or 5? e. How many are divisible by 4 and 5? f. How many are divisible by neither 4 nor 5? 6. Draw a decision tree (use teams A and B) to find the number of ways a playoff series can happen, where the winner is the first team to win 3 out of 5.

Answer 1

As it is HomeworkLib policy to answer one question per answer with four subquestions. But I am answering the first four sub-questions and request you to individually post rest of the questions.Thankyou.

a.) How many are divisible by 5?

• The numbers divisible by 5 are 180 from 100 to 999.
• Calculation: a =100, b=999.The formula for calculation is: x = [(b-a)/5]+1
• From the above formula the answer would be 180.

b.) How many are divisible by 4?

• Using the above same formula. we will get 225 numbers which will be divisible from 100 to 999.

c.) How many are not divisible by 5.

• For this, you just have to subtract the numbers divisible from 5 =180 from the total numbers in the series =899.
• The answer for this is 719.
• Hence, there are 719 numbers not divisible by 5.

e.) How many numbers are divisible by 4 and 5?

• It can be calculated using the Arithmetic progression formula which will give x = a+(n-1)d
• It will give the final answer as, 45.

Hence, these are all the answers.