If the probability that a randomly chosen 6 -digit number formed by using digits 1 and 8 only is a multiple of 21 is p , then 96 p is equal to _____.

Step-by-step solution

We have to choose 6 digit number by using 1   &   8 and it must be divisible by 21, So, equal number of digits 1 and 8 should be used to form a number divisible by 3 and 7 . (Or all the digits are either 1 or 8 ) In all cases whatever number is formed using six 1 ' or six 8 ' s or three 1 ' s + three 8 ' s, that number can be splited into sum of multiples of 1001 , 1008 , 8001 , 8008 (all of them are divisible by 7 ). So, all the numbers thus formed will be divisible by 21 , Example: 8