How many numbers greater than 40000 can be formed from the digits 2,4,5,5,7 ?

Step-by-step solution

The given digits are 2, 4, 5, 5, 7 . We need to form 5-digit numbers greater than 40000 . A 5-digit number is greater than 40000 if its first digit is 4, 5, or 7 . Case 1: The first digit is 4 . The remaining digits are 2, 5, 5, 7 . The number of ways to arrange these 4 digits is 4! 2! = 24 2 = 12 . Case 2: The first digit is 5 . The remaining digits are 2, 4, 5, 7 . The number of ways to arrange these 4 digits is 4! = 24 . Case 3: The first digit is 7 . The remaining digits are 2, 4, 5, 5 . The number of ways to a