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A 5 -digit number is formed using only the digits 1, 2 and 3 (repetition of digits is allowed). If the probability that the number formed is divisible by 36 is p , then the value of 243p is equal to

Correct answer

10

Step-by-step solution

Total number of 5 -digit numbers that can be formed using the digits 1, 2, 3 is 3^5 = 243 . For a number to be divisible by 36 , it must be divisible by both 4 and 9 . For divisibility by 4 , the number formed by the last two digits must be divisible by 4 . Using the digits 1, 2, 3 , the possible two-digit endings are 12 and 32 . Case 1: The number ends in 12 . The sum of the last two digits is 1 + 2 = 3 . For divisibility by 9 , the sum of all five digits must be a multiple of 9 . Since the maximum possible sum of

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