Six people on an elevator

[muzali]

Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?

Please explain your approach.

[logitech]

Six people are on an elevator that stops at exactly 6 floors. What is the probability that exactly one person will push the button for each floor?

Please explain your approach.

What is the OA muzali ?

muzali well there is not such a condition that everyone will stop at different floors so

for the first floor we have 6 people,
for the second floor we have AGAIN 6 people

you know where I am going with this:

6x6x6x6x6x6 = 6^6 ways

since we are asked:

What is the probability that exactly one person will push the button for each floor?


well lets call these 6 guys 1, 2,3,4, 5, 6

so they can stop like

6 5 4 3 2 1

3 4 5 1 2 6

and etc...

So we need to find all the possible ways that ONLY one person stops at each floor

6 persons for the first floor
5 persons for the second
4 persons for the third
....
1 person for the last floor

6x5x4x3x2x1 = 6!

So Probability is : 6!/6^6

[muzali]

OA is [spoiler]6!/(6^6)[/spoiler]