Permutations

can be written as


Number of divisor of = number of divisor of number of divisor of number of divisor of (49)

Number of divisor which are greater than 5 is = 24 - 1 = 23

We are to form 5-digit numbers using the digits 2, 5, 5, 6, 7. Since '5' is repeated, total permutations:

Now, to count numbers > 50000, the first digit must be either 5, 6, or 7. We’ll subtract the cases where the first digit is less than 5. Only digit > 5 is 2.
Case 1: First digit = 2
Remaining digits = 5, 5, 6, 7 → number of arrangements =
Required count: Total - Invalid =