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
1 hour = 60 minutes
1 hour:45 minutes
= 60 minutes:45 minutes
=12 minutes:9 minutes
2+3+2=7
Red has 3
Yellow has 2
2+3=5
5/7 is the fraction of red or yellow marbles in the bag.
Doubling would not change the answer
Since the y coordinate is the same for both points we only need to know the change in the x coordinates to find the distance between these two points.
5--12=17
So these two points are 17 units apart.
Answer
Are of the pool = w² + 5w (in square feet)
Explanation
Since the pool is rectangular in shape,
Area of the pool can be calculated using the formula for the area of a rectangle
Area of rectangle = length x width
Given,
Width of pool (Assume is same as height) = w
Length of pool= w + 5
Area = w * (w + 5)
= w² + 5w (in square feet)
where w is the width of the pool
