We're going to be using combination since this question is asking how many different combinations of 10 people can be selected from a set of 23.
We would only use permutation if the order of the people in the committee mattered, which it seems it doesn't.
Formula for combination:
Where 
represents the number of objects/people in the set and 
represents the number of objects/people being chosen from the set
There are 23 people in the set and 10 people being chosen from the set
Usually I would prefer solving such fractions by hand instead of a calculator, but factorials can result in large numbers and there is too much multiplication. Using a calculator, we get
Thus, there are 1,144,066 different 10 person committees that can be selected from a pool of 23 people. Let me know if you need any clarifications, thanks!
~ Padoru
Answer:
a) 0.778
b) 0.9222
c) 0.6826
d) 0.3174
e) 2 drivers
Step-by-step explanation:
Given:
Sample size, n = 5
P = 40% = 0.4
a) Probability that none of the drivers shows evidence of intoxication.
b) Probability that at least one of the drivers shows evidence of intoxication would be:
P(X ≥ 1) = 1 - P(X < 1)
c) The probability that at most two of the drivers show evidence of intoxication.
P(x≤2) = P(X = 0) + P(X = 1) + P(X = 2)
d) Probability that more than two of the drivers show evidence of intoxication.
P(x>2) = 1 - P(X ≤ 2)
![= 1 - [^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 * (0.4)^2 (0.6)^3]](https://tex.z-dn.net/?f=%20%20%3D%201%20-%20%5B%5E5C_0%20%20%280.4%29%5E0%20%20%280.6%29%5E5%20%2B%20%5E5C_1%20%20%280.4%29%5E1%20%20%280.6%29%5E4%20%2B%20%5E5C_2%20%2A%20%280.4%29%5E2%20%20%280.6%29%5E3%5D%20)
e) Expected number of intoxicated drivers.
To find this, use:
Sample size multiplied by sample proportion
n * p
= 5 * 0.40
= 2
Expected number of intoxicated drivers would be 2
Answer:
Therefore the third container contains 
= 43.23 % acid.
Step-by-step explanation:
Given that, One container is filled with the mixture that 25% acid. 55% acid is contain by second container.
Let the volume of first container be x cubic unit.
Since the volume of second container is 55% larger than the first.
Then the volume of the second container is
cubic unit.
cubic unit.
The amount of acid in first container is
cubic unit.
cubic unit.
The amount of acid in second container is
cubic unit.
cubic unit.
Total amount of acid 
cubic unit.
cubic unit.
cubic unit.
Total volume of mixture 
cubic unit.
cubic unit.
cubic unit.
The amount of acid in the mixture is
Therefore the third container contains acid.
Answer: R = {0, -3, -9, 5, 7}
Explanation: The range is the set of all y-coordinates for our ordered pairs.
So the range for this relation is {0, -3, -9, 5, 7}.
