Answer :
Final answer:
The number of 5-digit numbers divisible by 4 with digits from the set 1, 2, 3, 4, 5, with digit repetition allowed, is 625, derived by considering the divisibility rule for 4 and the choices for each digit position.
Explanation:
To find the number of 5-digit numbers divisible by 4 using the digits from the set 1, 2, 3, 4, 5, and allowing repetition of digits, we should focus on the property that a number is divisible by 4 if its last two digits form a number that's divisible by 4. We need to consider only the possibilities for the last two digits, since the first three digits can be any combination from the given set, each of which can occur in 5 ways.
From the set given, the possible pairs for the last two digits that are divisible by 4 are 12, 24, 32, 44, and 52. Since there are 5 choices for each of the first three positions and 5 valid combinations for the last two digits, we multiply them together to find the total number of such 5-digit numbers. So, the calculation is 5³ * 5, which is 125 * 5 = 625.
