Question

How many positive integers between 100 and 999 inclusive

a) are divisible by 7?

b) are odd?

c) have the same three decimal digits?

d) are not divisible by 4?

e) are divisible by 3 or 4?

f) are not divisible by either 3 or 4?

g) are divisible by 3 but not by 4?

h) are divisible by 3 and 4?

Solution

Verified
Step 1
1 of 10

DEFINITIONS

Division rule \textbf{Division rule }If a finite set AA is the union of pairwise disjoint subsets with dd elements each, then n=Adn=\dfrac{|A|}{d}

Product rule \textbf{Product rule }If one event can occur in mm ways AND a second event can occur in nn ways, the number of ways the two events can occur in sequence is then mnm\cdot n.

Subtraction rule \textbf{Subtraction rule } If an event can occur either in mm ways OR in nn ways (overlapping), the number of ways the event can occur is then m+nm+n decreased by the number of ways that the event can occur commonly to the two different ways.

Sum rule \textbf{Sum rule } If an event can occur either in mm ways OR in nn ways (non-overlapping), the number of ways the event can occur is then m+nm+n.

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy
Continue with GoogleContinue with Facebook

Recommended textbook solutions

Discrete Mathematics and Its Applications 7th Edition by Kenneth Rosen

Discrete Mathematics and Its Applications

7th EditionISBN: 9780073383095 (9 more)Kenneth Rosen
4,285 solutions
Discrete Mathematics 8th Edition by Richard Johnsonbaugh

Discrete Mathematics

8th EditionISBN: 9780321964687 (1 more)Richard Johnsonbaugh
4,246 solutions
Discrete Mathematics and Its Applications 8th Edition by Kenneth Rosen

Discrete Mathematics and Its Applications

8th EditionISBN: 9781259676512 (4 more)Kenneth Rosen
4,399 solutions

More related questions