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A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetitions.

The total number of ways this can be done is:

A. 216
B. 600
C. 240
D. 3125

Answer :

Final answer:

600 five-digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5 without repetition, that are also divisible by 3.

Explanation:

The subject of this question is combinatorics, part of Mathematics. We are asked to calculate the total number of ways a five-digit number divisible by 3 can be formed using the numbers 0, 1, 2, 3, 4, 5 without repetitions. The first step is to determine the total number of 5-digit numbers we can form from these six digits. We have 5 choices for the first digit (it cannot be 0), and then 5 choices for each remaining digit, which gives us 5*5*4*3*2 = 600 possibilities in total.

Next, we need to find the subset of these numbers that are divisible by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits 0, 1, 2, 3, 4, 5 is 15, which is divisible by 3. Therefore, any combination of these 5 digits will also be divisible by 3, regardless of order.

So, the answer to the question is (b) 600 five-digit numbers could be formed using the digits 0, 1, 2, 3, 4, 5 without repetition, that are also divisible by 3.

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Rewritten by : Barada

The answer is (a) 216