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3 years ago

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I want to read 4 books over the next month. My bookshelf has 12 different books. In how many ways can I choose which books to re

ad over the next month, without regard to the order that I read them?

1 answer:

shusha [124]3 years ago

8 0

Answer:

Step-by-step explanation:

You are going to choose 4 books in any order.

Four = 12! /(8!4!) Remember that order doesn't matter, so we have 12C4

495

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Consider the following.

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The slope is -5/6

Step-by-step explanation:

To find the slope of a line given two points, we use the formula

m= (y2-y1)/(x2-x1)

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=-5/(4+2)

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x=3

Step-by-step explanation:

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A circle has a radius that is 4 centimeters long. if a central angle has a measure of 3 radiants, what is the length of the arc

Romashka [77]

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3 years ago

Suppose we write the numbers $1,2,3,4,5,6$, and then color each number red or blue. The coloring is called factorific if there i

Oxana [17]

Answer:

The probability that his coloring is factorific is 0.28125

Step-by-step explanation:

For calculate the probability is necessary to identify the total number of ways to color the six number. This can be calculate with the rule of multiplication as:

2*2*2*2*2*2=64

Because we have 2 options to color every number.

For know the number of ways in which the coloring is factorific, first we need to identify the divisors of each number:

1: the divisor is 1

2: The divisors are 2 and 1

3: The divisors are 3 and 1

4: The divisors are 4, 2 and 1

5: The divisors are 5 and 1

6: The divisors are 6, 3 and 1

From these information we analyse that for made a factorific coloring, is necessary that the number 1 is color blue. Additionally if the number 4 is color blue, the number 2 needs to be color blue and if the number 6 is blue, the number 3 needs to be blue.

So, the number of ways in which we can create a factorfic number is determined by the following cases:

The number 2 is blue and the number 3 is blue: In this case we have 1 option for number 1, one for number 2 and 1 for number 3. Taking into account that the number 2 and 3 are blue, if the number 4 and 6 are blue or red doesn't change the fact that the coloring is going to be factorific. So, we have two options for number 3 and 2 options for number 6. Finally the color of the number 5 is independent of the colors of number 2 and 3, so we also have 2 options for coloring number 5 and the coloring is going to be factorific. Then the number of ways for this situation is calculate as:

<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 2 </u> *<u> 2 </u>* <u> 2 </u>= 8

number 1 number 2 number 3 number 4 number 5 number 6

At the same way we can calculate the following cases:

The number 2 is blue and the number 3 is red: If the number 3 is red, the coloring is only going to be factorific is number 6 is red. Then the number of ways for this situation is calculate as:

<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 2 </u> *<u> 2 </u>* <u> 1 </u>= 4

number 1 number 2 number 3 number 4 number 5 number 6

The number 2 is red and the number 3 is red: If the number 2 and 3 are red, the coloring is only going to be factorific is number 4 and 6 are red. Then the number of ways for this situation is calculate as:

<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 1 </u> *<u> 2 </u>* <u> 1 </u>= 2

number 1 number 2 number 3 number 4 number 5 number 6

The number 2 is red and the number 3 is blue: If the number 2 is red, the coloring is only going to be factorific is number 4 is red. Then the number of ways for this situation is calculate as:

<u> 1 </u>*<u> 1 </u>* <u> 1 </u> * <u> 1 </u> *<u> 2 </u>* <u> 2 </u>= 4

number 1 number 2 number 3 number 4 number 5 number 6

If we sum all the cases, we obtain 18 ways to make a factorific coloring. So the probability can be calculated as:

$P= \frac{18}{64} = 0.28125$

4 0

3 years ago