Question

The numbers a,b,c r selected by throwing a dice thrice then the probability that
a b c are in AP is

Answer 1

(a,b,c) can be

(1,2,3) -------- 2 possibilities (3,2,1) is the other order

(2,3,4) -------- 2 possibilities

..... --------- -do-

.....

(4,5,6) -------- -do-

it could be

(1,3,5) -------- 2 possibilities

(2,4,6) -------- 2 possibilities

or it could be

(1,1,1)

(2,2,2)

....

....

(6,6,6).

So total number of ways = 2*6 + 6 = 18.

so the probability=18/6^3=18/216