Jamestown Builders has a development of new homes. There are 6 different floor plans, 7 exterior colors,
and an option of either a one-car or a two-car garage. How many choices are there for one home?
(1 point)
84 choices
126 choices
15 choices
42 choices
126 choices
tell me how
To determine the total number of choices for one home, we need to multiply the number of options for each category.
There are:
- 6 floor plans to choose from
- 7 exterior colors to choose from
- 2 garage options (either a one-car or a two-car garage)
So the total number of choices is 6 x 7 x 2 = 84 x 2 = 126.
If no digit may be used more than once, how many 5-digit numbers can be formed using only the digits 3,
8, 1, 2, 5, and 7?
(1 point)
360 numbers
717 numbers
722 numbers
720 number
To determine the number of ways to form 5-digit numbers using digits 3, 8, 1, 2, 5, and 7 without repetition, we can use the permutation formula:
nPr = n!/(n-r)!
Here n = 6 (since there are 6 digits to choose from) and r = 5 (since we're forming 5-digit numbers).
So the number of 5-digit numbers that can be formed without repetition is:
6P5 = 6!/1! = 720
Therefore, the answer is 720 numbers. Option D is correct.