3 numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
Choose the correct choice from the following:
A) 3 / 40  B) 28 / 243  C) 3 / 25  D) 33 / 100  E) 64 / 125

Rationale: solution : total possible ways = 10 * 10 * 10 = 1000 case 1 : w = 0 . if x = 1 , then y can have 8 ways . if x = 2 , then y can have 7 ways and so on . so , no . of ways = 8 + 7 + . . + 1 case 2 : w = 1 . if x = 2 , then y can have 7 ways . if x = 3 , then y can have 6 ways and so on . so , no . of ways = 7 + 6 + . . + 1 there will be 8 cases in this way and they will follow a pattern which looks like this : no . of ways for case 1 : 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 no . of ways for case 2 : 1 + 2 + 3 + 4 + 5 + 6 + 7 no . of ways for case 3 : 1 + 2 + 3 + 4 + 5 + 6 no . of ways for case 4 : 1 + 2 + 3 + 4 + 5 no . of ways for case 5 : 1 + 2 + 3 + 4 no . of ways for case 6 : 1 + 2 + 3 no . of ways for case 7 : 1 + 2 no . of ways for case 8 : 1 ____________________________________________________________ total number of ways : 8 ( 1 ) + 7 ( 2 ) + 6 ( 3 ) + 5 ( 4 ) + 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) = 2 ( 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) ) = 2 ( 60 ) = 120 therefore , ans is 120 / 1000 = 3 / 25 . option c .
Answer: C