## Problem Of The Week 20

**A classroom has 4 tables, each of which has 4 chairs. There are 16 students in the class, 4 of whom are friends. If the teacher assigns the seats randomly to the students, what is the probability that the 4 friends will be sitting together at a table? **

*Tipster: To every probability question, there are two parts, one to find the total possible roster and the other, to find the ones which suit our case( or the ones which not). We can’t just find one and leave the other.*

The total possible selections possible are 16c4*12c4*8c4 and for the case when the four friends are sitting in the same bench, the number of possible selections are 4*12c4*8c4.So the probability is 4/16c4 which comes out to be 1/455.

Celebrating LifeSeptember 20, 2008 at 11:40 am

Total ways in which 16 students can be arranged in 16 seats = 16!

For four students to sit together we have to first select a table and then arrange the studens –

Total ways = 4*4!*12!

Hence probabilty = 4*4!*12!/16!= 1:455

AmitSeptember 20, 2008 at 5:40 pm

absolutely correct both of u !

outtimedSeptember 20, 2008 at 8:19 pm

IT can be answered in this way even :

The probability of choosing a table from 4 given table is 4c1 = 4

The probability of choosing the 4 friends out of 16 given people = (4/16)*(3/15)*(2/14)*(1/13)

Therefore the required probability = (4/16)*(3/15)*(2/14)*(1/13)*4

=1/455

riyaSeptember 23, 2008 at 8:10 pm