Number Theory#0
Number Theory
Level
3
The number of 5 digit +ve integers that are divisible by 3 can be formed using the digits 0,1,2,3,4 and 5 without repeating any of the digits are
The answer is 216.
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1 solution
A 5-digit number using those 6 digits with no repeats, means you must leave out 1 digit. The total of the digits is 15, a multiple of 3. Hence, it is also a multiple of 3 that is removed.
If the removed digit is 0, then there are 5 ! = 1 2 0 ways to arrange the digits. If the removed digit is 3, then there are only 4 × 4 ! = 9 6 ways to arrange the digits as it can't have a leading zero.
Therefore, 1 2 0 + 9 6 = 2 1 6 is the answer