Jamestown Builders has a development of new homes. There are six different floor plans, seven exterior colors, and an option of either a one-car or a two-car garage. How many choices are there for one home?

84 choices***
126 choices
15 choices
42 choices

2.If no digits may be used more than once , how many 5 digits can be formed using only the digits 3, 8,1,2,5 ,7?
360numbers
717numbers
722 numbers
720numbers***

agree on both

You are correct!!! :D

1. The number of choices for one home can be calculated by multiplying the number of options for each factor together. In this case, there are 6 floor plans, 7 exterior colors, and 2 options for the garage. Therefore, the total number of choices for one home is 6 x 7 x 2 = 84 choices.

2. To calculate the number of 5-digit numbers that can be formed using the given digits without repetition, we use the formula for permutations: nPr = n! / (n-r)!. In this case, we have 5 digits to choose from and we want to form a 5-digit number, so n = 5 and r = 5. Thus, the number of 5-digit numbers is 5! / (5-5)! = 5! / 0! = 5 x 4 x 3 x 2 x 1 = 120. Therefore, the number of 5-digit numbers that can be formed using the given digits without repetition is 120 numbers.

To find the answer to the first question, we need to multiply the number of choices for each category: floor plans, exterior colors, and garage options.

For floor plans, there are 6 choices.
For exterior colors, there are 7 choices.
And for the garage, there are 2 choices (one-car or two-car).

To find the total number of choices for one home, we multiply the number of choices for each category: 6 x 7 x 2 = 84.

Therefore, the answer is 84 choices.

To find the answer to the second question, we need to calculate the number of permutations using the given digits.

Since no digits can be used more than once, we have 5 digits to choose from (3, 8, 1, 2, 5) for each position in the 5-digit number.

To calculate the number of permutations, we multiply the number of choices for each position: 5 x 4 x 3 x 2 x 1 = 120.

However, since 0 is not included as one of the given digits, we need to subtract the possibility of having a number starting with 0.

Out of the 120 permutations, 1 of them would start with 0 (0 can only be the first digit). Therefore, we subtract this possibility to get the final answer: 120 - 1 = 119.

So, the answer is 119 numbers.

I apologize, but none of the options provided match the correct answer. It should be 84 choices for the first question and 119 numbers for the second question.