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Tatiana [17]
3 years ago
7

In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. Three of the 8 are in one family

, and want to sit together. How many ways can this happen?
Mathematics
1 answer:
lianna [129]3 years ago
4 0
There are 14 chairs and  8 people to be seated. But among the 8. three will be seated together:

So 5 people and (3) could be considered as 6 entities:

Since the order matters, we have to use permutation:

¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆  x 3! 

2,162,160 x 6 = 12,972,960 ways.

Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways
The 2nd has a choice among 13 ways
The 3rd has a choice among 12 ways
The 4th has a choice among 11 ways
The 5th has a choice among 10 ways
The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways
But the 3 (that formed one group) could seat among themselves in 3!
or 6 ways:

Total number of permutation = 2,162,160 x 6 = 12,972,960

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3 years ago
Whats the answer for this? 0.5x=24
Ganezh [65]

The answer for the expression 0.5x=24 will be x=48

<h3>What is a linear equation?</h3>

The linear equation is defined as the equation having a degree of one or the power of the variable will be one. Linear equation shows the staright line on the graph.

here the given equation is:-

0.5x=24

We can write 0.5 in fraction as 1/2

1/2x=24

x=48

Hence the answer for the expression 0.5x=24 will be x=48

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brainly.com/question/1884491

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8 0
2 years ago
HELP URGENT‼️‼️
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Answer:

The answer is 3 cups of orange juice.

Step-by-step explanation:

So basically it says every 1/4 cup of water, you need 3/4 cups of orange juice. Now, 1 cup of water is the same thing as 4/4 cups of water. To get to 4/4 from 1/4, you need to multiply 1/4 by 4. Because of that, you need to multiply 3/4 by 4 as well. 3/4 * 4 is 3, and that's how you get your answer.

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What is equivalent to (3 root 8^1/4 x) ?
vfiekz [6]

Answer:

The given expression is equivalent to 3(2^(3/8))x.

Step-by-step explanation:

The given expression (3 root 8^1/4 x) can be written as:

3√(8^(1/4))x

we know that 2^3 = 8

= 3√(2^(3/4))x

We know that √x = (x)^(1/2)

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Powers multiply with each other, 3*1/4*2 = 3/8

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