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
Hunter-Best [27]
3 years ago
10

A student dance committee is to be formed consisting of 2 boys and 4 girls. If the membership is to be chosen from 5 boys and 6

girls, how many different committees are possible?
Mathematics
1 answer:
Paha777 [63]3 years ago
7 0

150 different committees are possible

<h3><u>Solution:</u></h3>

Given that a student dance committee is to be formed consisting of 2 boys and 4 girls

The membership is to be chosen from 5 boys and 6 girls

To find : number of different possible committees

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 combination is given as:</u></em>

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

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

<em><u>We have to select 2 boys from 5 boys</u></em>

So here n = 5 and r = 2

\begin{aligned} 5 C_{2} &=\frac{5 !}{(5-2) ! 2 !}=\frac{5 !}{3 ! 2 !} \\\\ 5 C_{2} &=\frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1 \times 2 \times 1} \\\\ 5 C_{2} &=10 \end{aligned}

<em><u>We have to select 4 girls from 6 girls</u></em>

Here n = 6 and r = 4

\begin{aligned} 6 C_{4} &=\frac{6 !}{(6-4) ! 4 !}=\frac{6 !}{2 ! 4 !} \\\\ 6 C_{4} &=\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 4 \times 3 \times 2 \times 1}=15 \end{aligned}

<em><u>Committee is to be formed consisting of 2 boys and 4 girls:</u></em>

So we have to multiply 5 C_{2} and 6 C_{4}

5 C_{2} \times 6 C_{4}=10 \times 15=150

So 150 different committees are possible

You might be interested in
Andrew has a cell phone plan that provides 300 free minutes each month for
Mekhanik [1.2K]

Answer:

Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. For any minutes over 300, Andrew is charged $0.39 per minute. Let x be the number of minutes Andrew uses per month and f(x) be the charges based on Andrew's cell phone plan. If  then If  then first 300 minutes are free and each minute of next (x-300) minutes costs $0.39, therefore Hence, { 19 + 0.39(x - 300), x > 300

Hoped I helped

4 0
2 years ago
What is the x-intercept?​
Akimi4 [234]

x - intercept is (-4,0)

7 0
2 years ago
Read 2 more answers
Given an actual demand of 64, a previous forecast of 59, and an of .3, what would the forecast for the next period be using simp
BartSMP [9]

Answer: 60.5

Step-by-step explanation:

The forecast for the next period using the simple exponential smoothing method is given by:

D\times \alpha+F(1-\alpha) , where D= actual demand for the recent period, \alpha= smoothing factor, F= forecast for the recent period .

Given: D= 64, \alpha=0.34 , F= 59

The forecast for the next period  = 64\times0.3+59(1-0.3)

\\\\= 64\times0.3+59\times0.7\\\\=19.2+41.3\\\\=60.5

Hence, the forecast for the next period = 60.5

5 0
3 years ago
Identify the special name for ∠3 and ∠10
quester [9]

Answer:

square roots ?

Step-by-step explanation:

8 0
2 years ago
In Triangle XYZ, x = 5.2 inches, y = 9.8 inches and z=7.1 inches. Find the measure of
Oduvanchick [21]

Answer: 45

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • What does 4r+6 represent in the expression
    7·2 answers
  • Is this a function or no
    5·1 answer
  • Round 132874015 to the nearest hundreds-thousands.
    7·2 answers
  • STATS. How can we decide if an event that seems weird is actually unusual or fairly likely?
    5·1 answer
  • A geologist examines 6 seawater samples for lead concentration. The mean lead concentration for the sample data is 0.903 cc/cubi
    6·1 answer
  • Explain how you can use place value to describe how 0.05 and 0.005 compare
    6·1 answer
  • Edin has £300 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years. Ho
    11·1 answer
  • Please help me asap!!!
    7·1 answer
  • What type of function is represented by the graph below?
    11·1 answer
  • If Sabrina has seven letters, with no repeats, how many possible arrangements are there with the seven letters.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!