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
MakcuM [25]
3 years ago
14

Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo

se 2 books from the 7 recommended books?
Mathematics
1 answer:
Marianna [84]3 years ago
7 0

There are 21 ways Tim choose 2 books from the 7 recommended book

<em><u>Solution:</u></em>

Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

<em><u>The formula for combinations is:</u></em>

n C_{r}=\frac{n !}{r !(n-r) !}

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

<em><u>Substituting values in above formula, we get</u></em>

\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}

For a number n, the factorial of n can be written as,

n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1

Therefore, we get

7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21

Thus there are 21 ways Tim choose 2 books from the 7 recommended book

You might be interested in
How many solutions are there for the system x^2+4y^2=100 and 4y-x^2=-20
never [62]
There are 5 solutions for this system.

x^2 + 4y^2 = 100  ____1
4y - x^2 = -20  ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80   (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y :  y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2    x = /100 - 4y^2  (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
6 0
3 years ago
Please help:):):) Your awesome​
bonufazy [111]

Answer:

Q1: 11x - 8

Q2: 2x + 10

Q3: -3v + 12

3 0
3 years ago
Read 2 more answers
Which of these nonterminating decimals can be converted into a rational number?
ValentinkaMS [17]

A can be converted since it is a repeating decimal


4 0
3 years ago
The value of y varies directly with x. If x=3, then y=21. What is the value of x when y=105?
Aneli [31]

21/7 = 3 so then, 105/7 = x which is 15

3 0
3 years ago
What is 25% less than x
vladimir2022 [97]

Answer:

3/4x

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Find the area of the given figure.
    15·2 answers
  • Charlie wants to order lunch for his friends. He'll order sandwiches and a $2 kid's meal for his little brother. Charlie has $32
    15·2 answers
  • Why complex numbers comes in conjugates numbers?
    5·2 answers
  • Whats the area of 4.2 m and 3.6 m
    9·1 answer
  • Marshall works at an animal shelter. He makes sure all the cats are vaccinated. In July, 56 of the cats entering the shelter had
    14·1 answer
  • Find the circumference of the circle. R=6 ft please help
    15·1 answer
  • Find the unknown side length x. ​
    15·1 answer
  • Find the value of x?
    8·1 answer
  • Lexi rode her bicycle 3 1/4 miles from her house to the park. Then she rode 1 mile from the park to the library. How many miles
    11·2 answers
  • A , B , C , D ??????????????????????
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!