1. You have the numbers 1–24 written on slips of paper.If you choose one slip at random, what is the probability that you will not select a number which is divisible by 6?
a) 1/6
b) 5/6
c) 1/3
c) 2/3
2. There are 12 members of student council. Four of them will be elected into positions as officers: president, vice-president, secretary, and treasurer. How many specific ways can the council elect these four officers?
a) 16
b) 11,880
c) 495
d) 48
3. Is the following data set qualitative or quantitative
the number of hours spent to commuting to work by the employees of a company
a) qualitative
b) quantitative
1. How many numbers are divisible by 6?
6, 12, 18 and 24 Right?
There are 4 chances of getting a number divisible by 6 and 20 chances of getting a number NOT divisible by 6. So, you will have 20/24 which reduces to ???
2. You can use the counting principle here.
For president you have 12 choices
for vp you have 11
for secretary 10
for treasurer 9
You reduce by 1 because you one person is chosen leaving 1 less to choose from in each case. Multiply all of the numbers together and you should get the correct answer.
You can also look at this as a Permutation where you are choosing 4 out of 12.
3. Qualitative data would be something you can put into a category like: gender, eye color, hair color, etc.
Quantitative data is anything that you can measure and has units like miles, hours, seconds, age, height, weight, etc.
1. 5/6
2. 12 x 4 = 48 or 12 x 11 x 10 x 9 = 11,880 ?
3. quantitative
6, 12, 18, 24 is 4
4/24 = 1/6
1 - 1/6 = 5/6
permutations of 12 things 4 at a time is
n!/(n-r)! = 12!/8!
= 12 * 11 * 10 * 9
= 11,880
if it is a number I would call it quatitative.
1. To get the probability of not selecting a number divisible by 6, we need to determine the total number of slips that are not divisible by 6 and divide it by the total number of slips.
The numbers that are divisible by 6 are 6, 12, 18, and 24. So out of the 24 slips, there are 4 slips that are divisible by 6.
Therefore, the number of slips that are not divisible by 6 is 24 - 4 = 20.
The probability of not selecting a number divisible by 6 is given by the formula:
(Number of outcomes favorable for the event) / (Total number of possible outcomes)
In this case, the number of slips not divisible by 6 is the favorable outcome, and the total number of slips is the possible outcomes.
So, the probability of not selecting a number divisible by 6 is given by:
(20) / (24) = 5/6
Therefore, the answer is option b) 5/6.
2. To determine the number of specific ways the council can elect the four officers, we need to calculate the different possibilities for each position and multiply them together.
For the president position, there are 12 choices. Once a president is chosen, there are 11 remaining choices for the vice-president position. For the secretary position, there are 10 remaining choices, and for the treasurer position, there are 9 remaining choices.
To find the total number of specific ways to elect the four officers, we multiply the number of choices for each position together:
12 * 11 * 10 * 9 = 11,880
Therefore, the answer is option b) 11,880.
3. The given data set is the number of hours spent commuting to work by the employees of a company. This data set consists of numerical values, indicating the amount of time spent commuting.
Quantitative data involves numerical measurements or values that can be further analyzed mathematically or statistically. In this case, we have actual numbers of hours, so the data set is quantitative.
Therefore, the answer is option b) quantitative.