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
So Length * Width = 480 in. sq.
L=1 1/5 or 1.2W
substitute the L for 1.2W
1.2W*W=480 in sq
divide both sides by 1.2
w*w= 400
W²=400
square root of both sides
Width = 20 inches
Length= (1.2width) or (20*1.2)
Length=24 inches
Answer: x ≥ 6
<u>Step-by-step explanation:</u>
12 less <u>than</u> 5 times a number ≥ 6 more <u>than</u> twice the number
5x - 12 ≥ 2x + 6
Note: the word "than" switches the order of the terms.
5x - 12 ≥ 2x + 6
<u>-2x +12</u> <u>-2x +12 </u>
3x ≥ 18
<u>÷3 </u> <u> ÷3 </u>
x ≥ 6
Graph: 6 -----------→ the dot is closed (filled in) since it is "equal to"
144 - 56 = 88
88/144 simplified to -----> 11/18
