How many five digit numbers can be formed using every digit of 5, 6, 7, 8 and 9 which are divisible by 4?Options12243618

To find out how many five-digit numbers can be formed using every digit of 5, 6, 7, 8, and 9 that are divisible by 4, we need to understand the rule of divisibility by 4. A number is divisible by 4 if the number formed by the last two digits is divisible by 4.

Step 1: Identify the pairs of digits (from 5, 6, 7, 8, 9) that can form a number divisible by 4. They are 56, 68, and 96.

Step 2: For each pair, consider it as a single entity. Now, we have 4 entities (3 pairs and the remaining 2 digits).

Step 3: The number of ways to arrange these 4 entities is 4! (4 factorial) = 432*1 = 24.

Step 4: For each arrangement, the pair of digits can be arranged in 2! (2 factorial) = 2*1 = 2 ways.

Step 5: So, the total number of five-digit numbers that can be formed is 24 (from step 3) * 2 (from step 4) = 48.

Step 6: But we have 3 such pairs. So, the final answer is 48 * 3 = 144.

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