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.
ReplyDeleteTotal ways in which 16 students can be arranged in 16 seats = 16!
ReplyDeleteFor 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
absolutely correct both of u !
ReplyDeleteIT can be answered in this way even :
ReplyDeleteThe 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