Can anyone solve this? it's very urgent

A donut store has 11 different types of donuts. You can only buy a bag of 3 of them, where each donut has to be of a different t

MakcuM [25]

Answer:

$165$ .

Step-by-step explanation:

Since repetition isn't allowed, there would be $11$ choices for the first donut, $(11 - 1) = 10$ choices for the second donut, and $(11 - 2) = 9$ choices for the third donut. If the order in which donuts are placed in the bag matters, there would be $11 \times 10 \times 9$ unique ways to choose a bag of these donuts.

In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type $3 \times 2 \times 1 = 6$ times.

For example, if a bag includes donut of type $x$ , $y$ , and $z$ , the count $11 \times 10 \times 9$ would include the following $3 \times 2 \times 1$ arrangements:

$xyz$ .
$xzy$ .
$yxz$ .
$yzx$ .
$zxy$ .
$zyx$ .

Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count $11 \times 10 \times 9$ by $3 \times 2 \times 1 = 6$ to find the actual number of donut combinations:

$\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}$ .

Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of $3$ objects from a set of $11$ distinct objects:

$\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}$ .

5 0

2 years ago

Data set is normally distributed with a mean of 27 and a standard deviation of 3.5. Find the Z-score for a value of 25, to the n

Svetradugi [14.3K]

What is the standard deviation of the data set?

6, 4, 9, 5, 5, 4, 5

Round the answer to the tenths place.What is the standard deviation of the data set?

6, 4, 9, 5, 5, 4, 5

Round the answer to the tenths place.

Step-by-step explanation:

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3 0

2 years ago

Read 2 more answers

Skydiver is falling about 176 feet per second how many feet per minute

svlad2 [7]

1 minute has 60 seconds. So, we'll multiply the numerator and the denominator by 60.

176 feet/1 second = 10,560 feet/1 minute

6 0

3 years ago

Read 2 more answers

What is the value of x? Enter your answer in the box. x =

melisa1 [442]

The two angles are vertical angles, which means they are the same.

Set the two equations to equal and solve:

2x +2 = 3x -52

Subtract 2x from each side:

2 = x -52

Add 52 to each side:

x = 54

7 0

3 years ago

14 = 6+z / -2, Solve each equation. Check your solution.

aev [14]

Answer:

-16

Step-by-step explanation:

14=6+z/-2

14-6=z/-2

8=z/-2

z=8*-2

z=-16

5 0

3 years ago