Q1: 479 001 600 ways
Explanation:
You have 12 people, 12 seats, ¹²P₁₂ ways in arranging them, or essentially 12! ways
Q2: 1 036 800 ways
Explanation:
Let's break it up into two cases.
Case 1: BGBGBGBGBGBG
Case 2:GBGBGBGBGBGB
Let's deal with case 1, because case 2 will pop out. There are ⁶P₆ ways in sorting out the boys and ⁶P₆ ways in sorting out the girls, so for case 1, we'd have (⁶P₆)² ways in sorting out boys and girls in case 1.
This is exactly the same in case 2, so it'd be (⁶P₆)² ways in sorting out girls and boys in case 2.
So, (⁶P₆)² + (⁶P₆)² ways = 1 036 800 ways if they alternate
<span>As restaurant owner
The probability of hiring Jun is 0.7 => p(J)
The probability of hiring Deron is 0.4 => p(D)
The probability of hiring at least one of you is 0.9 => p(J or D)
We have a probability equation:
p(J or D) = p(J) + p(D) - p(J and D) => 0.9 = 0.7 + 0.4 - p(J and D)
p(J and D) = 1.1 - 0.9 = 0.2
So the probability that both Jun and Deron get hired is 0.2.</span>
