Again, there are 34 people in your class. Let’s say for some unknown reason that
ID: 3290063 • Letter: A
Question
Again, there are 34 people in your class. Let’s say for some unknown reason that I decide to make all 35 of us (the 34 students plus one instructor) stand in a line.
a) How many different ways can you form this line of 35 students? Note that order is important.
b) How many different ways can you form the line of 35 students, with the restriction that I am directly in front of you? (Hint: consider the case where I’m first and you’re second. Then, the case where I’m second and you’re third. Then keep going.)
c) How many different ways can you form the line of 35 students, with the restriction that I am directly behind you?
d) What’s the probability that, after forming this line, you and I are standing next to each other? That is, what’s the probability that I’m either in front of you, or behind you?
Explanation / Answer
a) Clearly, the number of ways, you can arrange 35 things, in a row = 35!
b) Since, I and you have to be together, consider us as one entity with you in front of me, then we've got 34 items to arrange, so , = 34!
c) Again, do the similar thing as in part (b), but this time me being in front, so the answer will be same = 34!
d) Number of ways we can be together = N = Ans(b)+Ans(c) = 2*34!
Total number of ways possible = M = Ans(a) = 35!
Probability = N/M = 2/35