Question

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

• A. 12
• B. 24
• C. 36
• D. 48

Hint:

When forming numbers from a set of digits, calculate the total permutations and subtract the unwanted cases (e.g., numbers starting with a certain digit).

Answer 1

The Correct Option is D

We are asked how many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7. Step 1: Count total number of numbers First, find the total number of distinct 5-digit numbers that can be formed from the digits 2, 4, 5, 5, 7. The total number of permutations of these digits is: \[ \frac{5!}{2!} = \frac{120}{2} = 60 \] Step 2: Subtract numbers less than 40000 Numbers less than 40000 must begin with 2. The number of distinct numbers that start with 2 is: \[ \frac{4!}{2!} = \frac{24}{2} = 12 \] Thus, the number of numbers greater than 40000 is: \[ 60 - 12 = 48 \] Thus, the correct answer is 48.