Given
Total members = 10
Find
probability that two of the students, Sofia and Victoria, will not be seated together.
Explanation
total arrangement of 10 members =
[tex]10![/tex]from the 10 members , taking the two students sofia ad victoria as one , so arrangement of 9 members is
[tex]9![/tex]these two students can be permuted among themselves in 2 ways
so , total arrangement =
[tex]2!\cdot9![/tex]therefore , the probability that two of the students, Sofia and Victoria, will be seated together. =
[tex]\frac{2\cdot9!}{10!}=\frac{2}{10}=\frac{1}{5}[/tex]so , required probability that two of the students, Sofia and Victoria, will not be seated together is 1 - 1/5 = 4/5
Final Answer
Therefore , the probability that two of the students, Sofia and Victoria, will not be seated together is 4/5
