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Question
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 ______.
Options
216
600
240
3125
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Solution
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 216.
Explanation:
We know that a number is divisible by 3 when the sum of its digits is divisible by 3.
If we take the digits 0, 1, 2, 4, 5, then the sum of the digits
= 0 + 1 + 2 + 4 + 5 = 12 which is divisible by 3
So, the 5 digit numbers using the digits 0, 1, 2, 4, and 5
TTh Th H T O
4 4 3 2 1
= 4 × 4 × 3 × 2 × 1
= 96
And if we take the digits 1, 2, 3, 4, 5, then their sum
= 1 + 2 + 3 + 4 + 5
= 15 divisible by 3
So, five-digit numbers can be formed using the digits 1, 2, 3, 4, 5 is 5! ways
= 5 × 4 × 3 × 2 × 1
= 120 ways
Total number of ways = 96 + 120
= 216.
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