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
blsea [12.9K]
3 years ago
6

Suppose you have 18 objects (10 of type A, 5 of type B, and 3 of type C). Objects of type A are indistinguishable from each othe

r; objects of type B are indistinguishable from each other; and objects of type C are indistinguishable from each other. In how many ways can you Pick 5 of the 18 objects (order does not matter)
Mathematics
2 answers:
Paladinen [302]3 years ago
5 0

Answer:

\binom{18}{5}= 8568

Step-by-step explanation:

Note that we have in total 18 items. Even though we are given information regarding the amounts of items per type, the general question asks the total number of ways in which you can pick 5 out of the 18 objects, without any restriction on the type of chosen items. Therefore, the information regarding the type is unnecessary to solve the problem.

Recall that given n elements, the different ways of choosing k elements out of n is given by the binomial coefficient \binom{n}{k}).

Therefore, in this case the total number of ways is just \binom{18}{5}=8568

maw [93]3 years ago
5 0

Answer:

Given:

Number of objects: n = 18

Type A objects: 10

Type B objects: 5

Type C objects: 3

To find:

In how many ways can you Pick 5 of the 18 objects (order does not matter)

Step-by-step explanation:

When the order does not matter we use Combination.

Formula to calculate combination:

C(n,r) = n! / r! ( n - r )!

n = 18

r = 5

Putting the values:

C(n,r)

= C(18,5)

= 18! / 5! ( 18 - 5 )!

= 18! / 5! ( 13 )!

= ( 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 ) / ( 5 * 4 * 3 * 2 * 1 ) * (13 * 12 * 11 * 10 *9* 8 * 7 *6 * 5 * 4 * 3 * 2 *1 )

Cancel 13!

= (18 * 17 * 16 * 15 * 14 ) / ( 5 * 4 * 3 * 2 * 1 )

= 1028160 / 120

= 8568

So you can pick 5 of the 18 objects in 8568 ways.

You might be interested in
3. Which statements about the line that passes through (-2, 0) and (2, -4) are true?
diamong [38]

Answer:

B, C, and D.

Step-by-step explanation:

Let's go through each answer choice.

A: To find the slope of a line from two points, we use this formula: (y_2-y_1)/(x_2-x_1). Plugging in the values (-2,0) and (2, -4), we get:

  • (-4-0)/(2+2)
  • -4/4
  • -1

Because option A says the slope is 1, but we got -1, option A is false.

B: To find the y-intercept, we use this formula: b = y_1 - m * x_1

  • b = 0 -(-1) * (-2)
  • b = 1 * (-2)
  • b = -2  

Since we know the value of b is the y-intercept, we could write the y-intercept as (0,-2). Therefore, option B is true.

C: The equation of a line (in slope-intercept form) is y = mx + b, where y - y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. Since we already solved for the y-intercept and slope, let's plug in those values:

  • y = mx +b
  • y = -x -2

As you can see, the equation we got here matches the one in option C, meaning it's true.

D: We know that a point is written like this: (x, y). If the x-coordinate is not zero but the y-coordinate is, then it's the x-intercept. Since the question says that (-2,0) is one of the points the line passes through, and option D says that the x-intercept is (-2,0), it's true.

8 0
2 years ago
Read 2 more answers
Rick made a paper football that was 1 1/6 inches long Carly made one that was 5/6 inches long how many longer was Rick's paper f
Alex17521 [72]
6 I believe if this is wrong sorry
5 0
3 years ago
Read 2 more answers
Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2
Levart [38]

Answer:

the desired equation is y = (-1/3)x + 6

Step-by-step explanation:

Let the given line be A:  y=3x+2

The slope of line A is m = 3.

The slope of any line B which is perpendicular to line A is the negative reciprocal of the slope of A:  m = -(1/3).

The particular perpendicular line that passes through (3, 5) is then

5 = (-1/3)(3) + b, which simplifies to 5 = -1 + b, or b = 6.

Thus, the desired equation is y = (-1/3)x + 6

7 0
2 years ago
Solve the equation by completing the square.<br><br> 3x^2 -6+9=0
Debora [2.8K]
The factored form would be (3x-9)(x-1)
The picture should help a bit
8 0
3 years ago
Read 2 more answers
If a polynomial function f(x) has roots 3 and square root of 7 what must also be a root of f(x)?
yuradex [85]
Whenever you have a root of sqrt #, you must have the matching - (or positive).
This is because when you take a square root you get two solutions a positive and a negative.
The answer is LETTER A
6 0
3 years ago
Read 2 more answers
Other questions:
  • Plz I really need help plz I'm begging you
    6·2 answers
  • What is the sum of the first 7 terms of this geometric sequence? 3, 9, 27, 81,
    5·1 answer
  • Select all the order pairs that satify the fucntion y = - 4x -1
    8·1 answer
  • Eugene wanted to make note cards by cutting pieces of paper in half. Before starting he got six more pieces to use. When he was
    13·2 answers
  • HURRY WHAT IS 1 + 1 ??????
    8·2 answers
  • Simplify root 32-6 divided by root 2 plus root 2​
    14·2 answers
  • What is the answer for this question <br>j-12=4<br>​
    9·1 answer
  • 6
    9·1 answer
  • PJ's Pizza Place bases its pizza prices on the size of the pizza and the number of toppings. The price of a medium pizza, in dol
    5·1 answer
  • What are the real solutions to the equation 5x² + 29x + 20 = 0?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!