Combinatoric Question: Elevator Odds in a Three Floor Building with 9 Apartments

[nhrock3]

in a three floor building on each store we have 3 appartments.
so in total we have 9 appartments.

every appartment has one person.

3 people enter the elevator(from the entrace of th building),each one goes to the floor he lives in.
A)
what are the odds that the elevator will stop at each floor
B)
what are the odds that the elevator will stop at two floors
C)
what are the odds that in the elavator would be 2 tenants from the second floor

regarding A:
we have 3 places to put 3 people so
for the first from we have 3 options the secong one 2 options and on the last floor we have only one person.

so its
$$\frac{3*2*1}{(_{3}^{9})}$$

correct?

and i don't know why all the oprions(the expresion in the denominator) is
9 over 3

 

[sunjin09]

in a three floor building on each store we have 3 appartments.
so in total we have 9 appartments.

every appartment has one person.

3 people enter the elevator(from the entrace of th building),each one goes to the floor he lives in.
A)
what are the odds that the elevator will stop at each floor
B)
what are the odds that the elevator will stop at two floors
C)
what are the odds that in the elavator would be 2 tenants from the second floor

regarding A:
we have 3 places to put 3 people so
for the first from we have 3 options the secong one 2 options and on the last floor we have only one person.

so its
$$\frac{3*2*1}{(_{3}^{9})}$$

correct?

and i don't know why all the oprions(the expresion in the denominator) is
9 over 3

Hint:
denominator: 3 person going to 9 places, i.e., choose 3 places from 9 for 3 person, does order matter?
numerator: 1st person has 9 places to go, 2nd has ? 3rd has ?

 

[nhrock3]

9*8*7 / (9 over 3)

regarding part B

we choose 2 floors from 3 (3 over 2)
we have three person the first has 6 places the second has 5 third is 4
correct?

(3 over 2)*6*5*4 /(9 over 3)

correct?