...lculus, he gets bored and writes all the permutations in "calculus". He is smart and can now write each permutation in 2 seconds. Find the positive differen ...ither end of the line, then the probability the person in front and behind Bob are both his friends is <math>\frac{m}{n},</math> for relatively prime posi ...

...lculus, he gets bored and writes all the permutations in "calculus". He is smart and can now write each permutation in 2 seconds. Find the positive differen ...tfrac{8!}{2!2!2!}=5040</math> permutations of "calculus", meaning it takes Bob <cmath>5040\cdot2 = 10080\text{ seconds}\implies \frac{10080}{60} = 168\tex ...