GMATinsight wrote:
Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is probability that none of the objects occupy the place corresponding to it's number?
A) 17/24
B) 3/8
C) 1/2
D) 5/8
E) 1/3
http://www.GMATinsight.comP(no object is in the right place) = (
# outcomes where no object is in right place)/(
TOTAL # number of outcomes)
ALWAYS begin with the denominator.
To understand WHY we should start with the denominator, see our free video -
http://www.gmatprepnow.com/module/gmat- ... /video/742TOTAL # number of outcomesWe can arrange the 4 objects in 4! ways (=
16 ways)
# outcomes where no object is in right placeSince, we know there are only 16 possible outcomes in TOTAL, it might not be a big deal just LIST the outcomes where no object is in right place.
We'll list the objects (1, 2, 3, and 4) in an order so that no number is in the correct place.
To begin, we'll place a 2 in the first position to get the following:
2134
2341
2413
There are 3 possible outcomes.
IF we place a 3 in the first position, we should also get 3 possible outcomes.
To confirm:
3142
3412
3421
Yep, 3 possible outcomes
IF we place a 4 in the first position, we should also get 4 possible outcomes.
To confirm:
4123
4312
4321
Yep, 3 possible outcomes
# of outcomes where no object is in right place = 3 + 3 + 3 =
9---------------------------
So, P(no object is in the right place) =
9/
24 = 3/8 = B