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
Answer:
1 out of 2
Step-by-step explanation:
Sorry if I’m wrong
Answer:
Empirical formula
0.34
0.33
0.33
A^c = event B or event C
Step-by-step explanation:
A = roommate A wins the game
P(A) = (Rock A and Scissors B) + (Scissors A and paper B) + (paper A and rock B)
P(A) = (0.36*0.53) + (0.32*0.25) + (0.32*0.22) = 0.3412
C = game ends in a tie :
P(C) = (RockA and rockB) + (ScissorsA and ScissorsB) + (ScissorsA and ScissorsB)
P(C) = (0.36*0.22) + (0.32*0.53) + (0.32*0.25) = 0.3288
P(B) = 1 - P(A) - P(C)
P(B) = 1 - 0.3412 - 0.3288
P(B) = 0.33
Complement of event A =event B or event C
<h3>
Answer: 8/15</h3>
Work Shown:
x = (1/3) divided by (5/8)
x = (1/3) * (8/5)
x = (1*8)/(3*5)
x = 8/15
