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vodka [1.7K]
3 years ago
6

In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. There is someone with a very bad

cough who must sit at least one seat away from anyone else. How many ways can this happen?
Mathematics
1 answer:
diamong [38]3 years ago
5 0

Answer: 12,972,960

Step-by-step explanation: 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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Answer:

30 out of 40: 75%

40 out of 50: 80%

40 out of 50 is the better score

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DaniilM [7]

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2 years ago
a college freshman started the year with $4000 in spending money and after three months,she has $2800 left.assume that she will
gulaghasi [49]
Let's find out how much she spent every month.

4000 (starting money) - 2800 (remaining money) = 1200 spent over 3 months

1200/3 = 400 per month was spent

So if she continues to spend 400 a month?

How many months are left? 12 (months of the year) - 3 (months she already spent) = 9

So 9 (remaining months) * 400 (amt per month) = 3600 she'll spend at the going rate over 9 months.

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3 0
3 years ago
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6 0
3 years ago
F(x)=x^2+8x-10 find f(a)+5
Papessa [141]

Answer:

We conclude that:

f(a) + 5 = a² + 8a - 5

Step-by-step explanation:

Given

The function is given by

f(x) = x²+8x-10

To determine

f(a)+5

In order to determine f(a)+5, first, we need to determine f(a).

Now substitute x = a in the function f(x) = x²+8x-10

f(a) = (a)² + 8(a) - 10

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f(a) + 5 = (a² + 8a - 10) + 5

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f(a) + 5 = a² + 8a - 5

4 0
3 years ago
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