Lesson 7 So Many Possibilities! Develop Understanding
Mark each statement with Always true, Sometimes true, or Never true. If your answer is “Sometimes true” give an example of when it is not true and an example of when it is true.
1.
The product of any number raised to a positive exponent is larger after the multiplication.
Always true
Sometimes true
Never true
2.
The quotient of an integer divided by an integer is always a smaller integer.
Always true
Sometimes true
Never true
3.
A fraction multiplied by a fraction always makes a smaller fraction.
Always true
Sometimes true
Never true
4.
The quotient of any number,
Always true
Sometimes true
Never true
5.
Two fractions each with a numerator of
Always true
Sometimes true
Never true
6.
How many pin numbers can be made from four digits?
7.
How many 4-digit pin numbers can be made if repeated digits are not allowed?
8.
What is the probability that a randomly generated 4-digit pin number will have no repeated digits?
9.
In some races, runners are given prizes for first, second, and third place. If there are
10.
If there are
11.
How many 7-letter passwords can be made if only lower-case letters are used?
12.
How many 7-letter passwords can be made if each position can be either a lower-case letter or a number?
13.
Use the Fundamental Counting Principle to explain why many sites require passwords to include at least one upper case letter, one number, and a special symbol like #,*, or &.
14.
How many possible rearrangements of the letters A, H, M, T are there if none of the letters are repeated? What is the probability that the word “math” is randomly selected from the group of rearrangements?
Solve for