3 says, "i can divide You"

Probability Level 2

A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is.

216 600 3125 240

Arpit Dhimanj by Arpit Dhimanj , 23, India

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1 solution

Utkarsh Goel
Jul 1, 2014

For a number to be divisible by 3, its sum of digits should be divisible by 3. For a five digit number, with the above choices, the number can be made by only excluding either 3 or 0. (0+1+2+3+4+5=15, 15-0=15, 15-3=12)

Excluding 0, numbers possible = 5! =120

Excluding 3, 0 cannot be used as the first digit, hence numbers possible = 4x4x3x2x1=96 Total =120+96= 216

7 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it in the same way except that I used Python to obtain the two combinations of digits that would yield numbers divisible by 3:

>>> c=combinations(range(6),5)

>>> for comb in c:

... if sum(comb)%3==0:

... print comb

...

(0, 1, 2, 4, 5)

(1, 2, 3, 4, 5)

Bill Bell - 6 years, 9 months ago

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