Question

Four people each roll a four die once. find the probability that atleast two people will roll the same number

Answer 1

Let's first find the probability that all the people get different numbers.

Outcome of each die can be any of the 6 numbers. Therefore,

Total number of outcomes =64

First die can give any of the 6 numbers

Second die can give any of the remaining 5 numbers

Third die can give any of the remaining 4 numbers

Fourth die can give any of the remaining 3 numbers

Therefore, total favorable outcomes 6×5×4×3

P(all people get different numbers) =6×5×4×364=518

P(at least 2 people get the same number) =1−518=1318

Answer 2

here is your answer.....

probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6)
suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.
so 2nd time probability=5C1 i.e. (2,3,4,5,6)
same way 3rd and 4th time probability=4C1 and 3C1 respectively.

probability that no one rolls the same no. = 6*5*4*3

and total possibility =6^4 
p(same number)= 6*5*4*3/ 6^4
= 5/18

p(no same number will roll)=1-5/18
=13/18