The number of five-digit numbers formed using the digits 2, 3, 5, 7, 9 without repetition and which are greater than 24000 are

Step-by-step solution

The total number of five-digit numbers that can be formed using the digits 2, 3, 5, 7, 9 without repetition is 5! = 120 . For a number to be less than 24000 , it must start with 2 and the second digit must be less than 4 . From the given digits, the only possible second digit less than 4 is 3 . Thus, the numbers less than 24000 must be of the form 23XXX . The remaining three positions can be filled by the remaining three digits ( 5, 7, 9 ) in 3! = 6 ways. Therefore, the number of five-digit numbers greater than 240