Six friends Rita, Anika, Zara, Lima, Arif, and Sayeed sit randomly in a row of six chairs. What is the probability that Rita and Anika do not sit next to each other?

Question: Six friends Rita, Anika, Zara, Lima, Arif, and Sayeed sit randomly in a row of six chairs. What is the probability that Rita and Anika do not sit next to each other?

Solution:
Total number of possibilities = 6! = 720

Number of possibilities where Rita and Anika sit together = 5! × 2!
​= 120 × 2
= 240

So the possibilities where Rita and Anika do not sit together = 720 - 240
= 480

∴Probability that Rita and Anika do not sit next to each other = 480/720
= 2/3