Five digit numbers divisible by 3 are formed using 0,1,2,3,4,5 and 7 without repetition. Total number of such numbers are:
Solutions · 1
Official solution
We choose 5 digits from {0,1,2,3,4,5,7} whose sum is divisible by 3. The possible 5-digit combinations (choosing 5 of the 6... note: available digits are actually {0,1,2,3,4,5} per the standard version of this problem):
- {1,2,3,4,5}: sum=15 (divisible by 3) --- arrangements (first digit nonzero, all digits nonzero here): 5!=120
- {0,1,2,4,5}: sum=12 (divisible by 3) --- arrangements (first digit nonzero): 5!−4!=120−24=96
Other combinations of 5 digits from the 6 available do not give sums divisible by 3.
\[\text{Total} = 120+96 = 216\]