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3 years ago

In how many ways can a committee of 3 men and 2 women be formed from a group of 9 men and 10 women?

Mathematics

1 answer:

Setler [38]3 years ago

6 0

Answer:

first you have to find the number of ways 3 men can be chosen, then the number of ways 2 women can be chosen, and then you need to multiply these numbers together to get the number of ways because multiplication will show the total arrangements possibilities. use combination since order does not matter.

number ways for 2 out of 10 women total: 10 choose 2= 45

number of ways for 3 out of 9 men total: 9 choose 3= 84

84x45= 3780

3780 total ways

number of ways

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Hcf and lcm of 54,18,90

Inessa05 [86]

HCF is 6

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3 years ago

Do 4x and 15 + x have the same value when x is 5? How do you know?

alexandr402 [8]

Answer:

yes

Step-by-step explanation:

If x = 5,

4x=4*5=20

15+x=15+5=20

They're both the same.

4 0

3 years ago

Read 2 more answers

Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

It can be clearly seen that:

$\angle DFE = \angle E =90-\dfrac{y}{2}$

The two angles of $\triangle EDF$ are equal hence $\triangle EDF$ is isosceles.

8 0

3 years ago

John is making baked goods for a party. He can either make muffins or bread, and he can use blueberries, bananas, apples, or cho

Margarita [4]

The total number of possible choices that John had for making baked goods for the party is 8.

<h3>What is Combination?</h3>

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

$^nC_r = \dfrac{n!}{r!(n-r)!}$

where,

n is the number of choices available,

r is the choices to be made.

We know that the number of choices with John for his baked goods is only two which are muffins or bread, therefore, the choices of the baked good can be written as $^2C_1$ .

Also, the number of choices with John for flavors is four which are blueberries, bananas, apples, or chocolate chips, therefore, the choices of the flavor can be written as $^4C_1$ .

Now, the total possible choices that John had

= The choices of the baked good x The choices of the flavor

$=\ ^2C_1 \times ^4C_1\\\\=\ 8$

Hence, the total number of possible choices that John had for making baked goods for the party is 8.

Learn more about Combination:

brainly.com/question/11732255

8 0

2 years ago

2. Felicia took out a simple interest loan at 12 percent interest for 6 months. Her previous balance is $2,460,

marishachu [46]

Answer:

Answer:

28+66+86=180

180=180

Step-by-step explanation:

Since there is a triangle and the 3 measures from the angles we can find the value of x using the hint given that the sum of the interior angles must be 180°

Write the equation

\begin{gathered}x+(2x+10)+(3x+2)=180\\\end{gathered}

x+(2x+10)+(3x+2)=180

Simplify left side of the equation

\begin{gathered}6x+12=180\\\end{gathered}

6x+12=180

Solve equation for x

\begin{gathered}6x=180-12\\6x=168\\x=28\end{gathered}

6x=180−12

6x=168

x=28

Replace x into the 3 angles and find their respectives values

\begin{gathered}A=x\\A=28\\\\B=2x+10\\B=2*28+10\\B=56+10\\B=66\\\\C=3x+2\\C=84+2\\C=86\end{gathered}

A=x

A=28

B=2x+10

B=2∗28+10

B=56+10

B=66

C=3x+2

C=84+2

C=86

Check if the answers are correct

\begin{gathered}28+66+86=180\\180=180\end{gathered}

28+66+86=180

180=180

PLEASE MARK ME AS BRAINLIEST

6 0

3 years ago

In how many ways can a committee of 3 men and 2 women be formed from a group of 9 men and 10 ​women?

In how many ways can a committee of 3 men and 2 women be formed from a group of 9 men and 10 women?