All categories

3 years ago

How many ways are there to choose a committee of 7 people from a group of 10 people?7201208405040?

Mathematics

1 answer:

lyudmila [28]3 years ago

5 0

Answer: 120

---------------------------------------------------------------------------------------

Explanation:

We have seven slots to fill. Let's call the slots A, B, C, D, E, F, G

There are 10 choices for slot A

There are 9 choices for slot B

There are 8 choices for slot C

There are 7 choices for slot D

There are 6 choices for slot E

There are 5 choices for slot F

There are 4 choices for slot G

We count down because each previous slot reduces the pool to choose from. Multiply those values out: 10*9*8*7*6*5*4 = 604800

Now divide that result by 5040. Why 5040? Because this is the number of ways to arrange 7 people within a single grouping. Note how 7! = 7*6*5*4*3*2*1 = 5040. W're dividing because order does not matter for any committee.

So we have 604800/5040 = 120 which is the answer we want

---------------

Side note: We could use the alternate route of the nCr combination formula

nCr = (n!)/(r!*(n-r)!)

where n = 10 and r = 7

You might be interested in

For the past three months, Grace used her cell phone for 43 minutes, 62 minutes, and 57 minutes how many minutes would she have

mina [271]

Answer:1

Step-by-step explanation:

Her average over those three months already is 54 so she has and average on 1 min left

8 0

3 years ago

The perimeter of a building is 900 feet. If the length of the building is 400 feet, find the width. How many lights will be need

Helen [10]

Answer:

The width of the building is 50 lamps and 60 lamps will be needed.

Step-by-step explanation:

The perimeter is computed by the sum of the sides of the building, since the length and width are equal on the oposite sides of the building, the perimeter is given by:

perimeter = 2*length + 2*width

900 = 2*(400) + 2*width

2*width + 800 = 900

2*width = 900 - 800

2*width = 100

width = 100/2 = 50 feets

To know how many lights bulbs will be needed we need to take the perimeter of the building and divide it by the space between the lamps. We have:

number o lamps = 900/15 = 60 lamps

8 0

3 years ago

Read 2 more answers

HELP ME ASAP

Soloha48 [4]

Answer:

An article explaining your ideas on how to best rescue endangered loggerhead turtle eggs

Step-by-step explanation:

In the problem and solution organization pattern, it is all about the ability to determine the problems affecting the organisation as well as proffer solutions on how to solve those problems. This would then lead to minimizing cost and maximizing profits. <em>The example above which is about ideas on how to rescue endangered loggerhead turtle eggs is following same pattern.</em>

8 0

3 years ago

Jackson used 8/9 of a case of soda to fill 1/3 of the soda machine. How many cases does it take to fill the soda machine?

lorasvet [3.4K]

Jackson used 8/9 of a case of soda to fill 1/3 of the soda machine.
how many cases does it take to fill the soda machine = ?
1/3 means three parts of the soda machine, it means if we fill with 8/9 of a case three times soda machine will be full so,
8/9 + 8/9 + 8/9 = 24/9
it means it takes the case of soda between 2 and 3.
2.667 approx. cases of soda it take to fill the soda machine.

8 0

3 years ago

A study investigated whether price affects people's judgment. Twenty people each tasted six cabernet sauvignon wines and rated h

patriot [66]

Answer:

t=5.5080( to 3 d.p)

Step-by-step explanation:

From the data given,

n =20

Deviation= 34/20= 1.7

Standard deviation (sd)= 1.3803(√Deviation)

Standard Error = sd/√n

= 1.3803/V20 = 0.3086

Test statistic is:

t = deviation /SE

= 1.7/0.3086 = 5.5080

ndf = 20 - 1 = 19

alpha = 0.01

One Tailed - Right Side Test

From Table, critical value of t =2.5395

Since the calculated value of t = 5.5080 is greater than critical value of t = 2.5395, the difference is significant. Reject null hypothesis.

t score = 5.5080

ndf = 19

One Tail - Right side Test

By Technology, p - value = 0.000

Since p - value is less than alpha , reject null hypothesis.

Conclusion:

From the result obtained it can be concluded that ,the data support the claim that the mean rating assigned to the wine when the cost is described as $90 is greater than the mean rating assigned to the wine when the cost is described as $10.

5 0

3 years ago