QJEEM02Ma8c52: JEE Main 2002 Mathematics - Class 11 JEEM02Ma8c52 Solution: Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4…

Note : For a number to be divisible by 3, the sum of digits should be divisible by 3.

Here given numbers are 0, 1, 2, 3, 4 and 5. Out of those 6 numbers possible sets of 5 numbers are (1, 2, 3, 4, 5) and (0, 1, 2, 4, 5) whose sum are divisible by 3.

Set 1 : Set is = (1, 2, 3, 4, 5). Sum of digits = 1 + 2 + 3 + 4 + 5 = 15 (Divisible by 3)



So total no of arrangement = 1$$\times$$2$$\times$$3$$\times$$4$$\times$$5 = 5!

Set 2 : Set is = (0, 1, 2, 4, 5). Sum of digits = 0 + 1 + 2 + 4 + 5 = 12 (Divisible by 3)

So total no of arrangement = 4$$\times$$4$$\times$$3$$\times$$2$$\times$$1 = 4.4!

$$\therefore$$ Total arrangement = 5! + 4.4! = 216