vikram4689 wrote:In a certain three-story apartment building, there are 11 tenants on the first floor, 3 tenants on the second floor, and 7 tenants on the third floor. If two tenants are selected at random to be co-chairs of the tenants' association, what is the probability that the two co-chairs will be from adjacent floors?
(A) 7/60
(B) 9/70
(C) 11/60
(D) 11/70
(E) 9/35
We can also solve this question using counting techniques (as is the case with many probability questions).
In this case, it might be useful to use the complement. That is P(co-chairs from adjacent floors) = 1 -
P(co-chairs not from adjacent floors)
P(co-chairs not from adjacent floors) =
(# of outcomes where selections are not adjacent)/
(total # outcomes)
As always, calculate the denominator first.
total # outcomes = total number of ways to select 2 tenants from 21 tenants
This can be accomplished in 21C2 ways (this is combination notation)
# of outcomes where selections are not adjacent
There are two ways this can happen:
1) The two people are selected from floor #1 and/or floor #3
2) The two people are selected from floor #2
1) The two people are selected from floor #1 and/or floor #3
To determine the number of possible outcomes, take the 18 tenants from floors 1 and 3, and select 2 of them.
This can be accomplished in 18C2 ways
2) The two people are selected from floor #2
To determine the number of possible outcomes, take the 3 tenants from floor #2, and select 2 of them.
This can be accomplished in 3C2 ways
So,
P(co-chairs not from adjacent floors) =
(18C2 + 3C2)/
(21C2)
=
(153 + 3)/
(210)
= 156/210
=
26/35
And finally, P(co-chairs from adjacent floors) = 1 -
P(co-chairs not from adjacent floors)
= 1 -
26/35
= 9/35
=
E
Cheers,
Brent
If anyone is interested, we have a free video on calculating combinations in your head:
https://www.gmatprepnow.com/module/gmat-counting?id=789
