1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Reptile [31]
2 years ago
5

Help pls I'll give 25 points

Mathematics
1 answer:
RideAnS [48]2 years ago
5 0

Answer:

\text{C. }60

Step-by-step explanation:

<u>Question from image</u>:

"The digits 1, 2, 3, 4, and 5 can be formed to arrange 120 different numbers. How many of these numbers will have the digits 1 and 2 in increasing order? For example, 14352 and 51234 are two such numbers."

Let's start by taking a look with the number 1. There are four possible places 1 could be, because there needs to be space for the 2 after it.

Checkmarks mark where the 1 can be, the <em>x</em> marks where it cannot be.

\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{X}

Let's start with the first position:

\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}\:\underline{\#}

There are four places the 2 can be. For each of these four places, we can arrange the remaining 3 digits in 3!=6 ways. Therefore, there are 4\cdot 6=\boxed{24} possible numbers when 1 is the first digit of the number.

Continue this process with the remaining possible positions for 1.

Second position:

\underline{X}\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}

There are three places the 2 can be, since the 2 must be behind the 1. For each of these three places, the remaining 3 digits can be arranged in 3!=6 ways. Therefore, there are 3\cdot 6=\boxed{18} possible numbers when 1 is the second digit of the number.

The pattern continues. Next there will be 2 places to place the 2. For each of these, there are 3!=6 ways to rearrange the remaining 3 digits for a total of 2\cdot 6=\boxed{12} possible numbers when 1 is the third digit of the number.

Lastly, when 1 is the fourth digit of the number, there is only 1 place the 2 can be. For this one place, there are still 3!=6 ways to rearrange the remaining three numbers. Therefore, there are 1\cdot 6=\boxed{6} possible numbers when 1 is the fourth digit of the number.

Thus, there are 24+18+12+6=\boxed{60} numbers that will have the digits 1 and 2 in increasing order, from a set of 120 five-digit numbers created by the digits 1 through 5, where no digit may be repeated.

You might be interested in
How to add 59.5 +30 show process of adding it​
mojhsa [17]

Answer:

89.5

Step-by-step explanation:

59.5

30.0

89.5

8 0
2 years ago
Will mark brainliest and will give 15 points!!!!
Lerok [7]

Answer:

There is 1 way to vote for 0 people. There are 8 ways to vote for 1 person. There are 8⋅7/ 2 ways to vote for 2 people. There are 8⋅7⋅6 /2⋅3 ways to vote for 3 people. There are 8⋅7⋅6⋅5/ 2⋅3⋅4 ways to vote for 4 people. This is all because you can choose people but there are ways you can order the people.  

Does this help

8 0
3 years ago
Anyone help?<br><br> What is the derivative of x^2 + 2x - 4?<br><br> Thanks!
castortr0y [4]
Let's take the derivative of each term one by 1

x^2
Apply the power rule for derivatives.
2x^(2-1) = 2x
You get 2x.

2x
Apply the power rule (x^1) and the constant multiple rule.
2 * x^(1-1) = 2 * x^0 = 2
You get 2.

-4
The derivative of a constant is 0.

Put that together and you get 2x + 2

Have an awesome day! :)
4 0
2 years ago
Read 2 more answers
the midpoint of AB has coordinates (4, -9). Endpoint A has coordinates (-3,-5). what are the coordinates of B
olchik [2.2K]
The coordinates for other endpoint is (5,-23)

3 0
2 years ago
Read 2 more answers
A ball has a radius of 5 inches. What is the volume it can hold
Nataliya [291]
A ball is a Sphere sooooo......
V=4/3 \pi r^{3}
And when you enter the radius.....
The answer will be about 523.6 inches
5 0
3 years ago
Other questions:
  • A company's profit is described by the equation P(x)=-5x^2+300x+15,000
    7·2 answers
  • Real life Applications of Polynomials?
    8·1 answer
  • When data is displayed with a scatter plot, it is often useful to attempt to represent that data with the equation of a straight
    15·1 answer
  • What is 0.08333333333 as a fraction?
    9·1 answer
  • Can somebody help me
    9·1 answer
  • Given the list of ordered pairs, what is the x intercept (8,10),(3,-4),(0,8),(4,-3),(9,0)
    6·1 answer
  • ZA and ZB are complementary. If m ZA = (x - 6) º<br> and m2B = (3x) °, find the value of x.
    7·2 answers
  • What is the equation of the graph in slope-intercept form?
    14·1 answer
  • Pls help it’s 6th grade math
    14·2 answers
  • Y=(x-5)(2x+3) x intercept? HELPPP
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!