Answer:
They can be seated in 120 differents ways.
Step-by-step explanation:
Taking into account that there are 3 couples and every couple has an specific way to sit, for simplify the exercise, every couple is going to act like 1 option and it's going to occupy 1 Place. If this happens we just need to organize 5 options (3 couples and 2 singles) in 5 Places (3 for a couple and 2 for the singles)
It means that now there are just 5 Places in the row and 5 options to organized. So the number of ways can be calculated using a rule of multiplication as:
<u> 5 </u>*<u> 4 </u>* <u> 3 </u> * <u> 2 </u> * <u> 1 </u> = 120
1st place 2nd Place 3rd place 4th Place 5th Place
Because we have 5 options for the 1st Place, the three couples and the 2 singles. Then, 4 options for the second Place, 3 options for the third place, 2 for the fourth place and 1 option for the 5th place.
Finally, they can be seated in 120 differents ways.
h = t - 15
h + t = 33
Because we have a value of h, we can plug it into the second equation to solve for t.
t - 15 + t = 33
Add 15 to both sides.
t + t = 48
Combine like terms.
2t = 48
Divide both sides by 2.
t = 24
<h3>Thomas's age is 24.</h3>
Please find the attached file for a better understanding of the explanation given here.
the attached diagram is a generated image of the first fifteen rows of a pascal's triangle. As can be seen from the image, the least four-digit number in the first fifteen rows of pascal's triangle is 1001.
In the diagram attached that number is present in the very last row and is highlighted using a yellow rectangle.
I believe the answer is
f(x)=3x -6
Hope this helped.
