Three new students are to be assigned at random to 5 empty dormit

Question

Three new students are to be assigned at random to 5 empty dormitory rooms. What is the probability that all the three students will be assigned to the same room?

(A)  \frac{1}{5}

(B)  \frac{1}{10}

(C)  \frac{1}{15}

(D)  \frac{1}{25}

(E)  \frac{1}{30}

firas92 · Answer

Probability that all the three students will be assigned to the same room 
= Number of ways the students are in the same room / Total Number of ways of assigning the rooms

Each student has 5 ways to be assigned a room and so the total number of ways to assign the rooms = 5*5*5 = 125

There are 5 ways in which the students can be assigned the same room (All in room 1, All in room 2, All in room 3, All in room 4 or All in room 5)

So the required probability is 5/125 = 1/25

Answer is  (D)

Hit Kudos if this helped!

philipssonicare · Answer

First student can go to any room (1/1). Second student has a 1/5 chance of going to the same room. Third student has a 1/5 chance of going to the same room
1/1 * 1/5 *1/5=1/25
 D

Three new students are to be assigned at random to 5 empty dormit

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards