Let A A denote the set of all 4 -digit natural numbers with no digit being 0 . Let B ⊂ A consist of all numbers x such that no permutation of the digits of x gives a number that is divisible by 4 . Then the probability of drawing a number from B with all even digits is

Step-by-step solution

All even digit numbers in B = 2 , 4 , 6 , 8 fav : forming a 4 digit nos with all digit is even and not divisible by 4 2222 ,   6666 ,   2266 , 4 ! 2 ! 2 ! = 6 cases 2226 ,   2666 4 ! 3 ! = 4 cases 4 ! 3 ! = 4 cases Total = 1 + 1 + 6 + 4 + 4 = 16 cases Total : forming a 4 -digit no. from 1 , 2 , … , 9 but not divisible by 4 C - 1 all 4 digit are add = 5 4 = 625 C - 2 all 4 digit are even = 16 C - 3 one even and 3 odd you can not take 2 or 6 as one of even digit 12 , 16 , 32 , 36 , … all ar