Question

3 Dice are rolled, what is the probability that they are all different numbers AND one of them lands on a 6?

Answer 1

P[ there are all different numbers AND one of them lands on a 6 ] = P[ a die throwing 6 ]*P[ remaining two die throwing any number other than 6 ]*Number of ways these three numbers can be arranged

Number of ways these three numbers can be arranged = 3! = 3*2*1

P[ a die throwing 6 ] = 1/6

P[ remaining two die throwing any number other than 6 ] = (5*4)/36 = 20/36

P[ there are all different numbers AND one of them lands on a 6 ] = (6)*(1/6)*(20/36)

P[ there are all different numbers AND one of them lands on a 6 ] = 0.55