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Permutation and Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPermutation and Combinations1 Mark
MCQ
Choose the correct answer.
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.
✓

Answer

  1. 216

Solution:

We know that a number is divisible by 3 if the sum of its digits is divisible by 3.

Now sum of the given six digits is 15 which is divisible by 3. So to form a number of five-digit which is divisible by 3 we can remove either ‘O’ or ‘3’. If digits 1, 2, 3, 4, 5 are used then number of required numbers = 5!

If digits 0, 1, 2, 4, 5 are used then first place from left can be filled in 4 ways and remaining 4 places can be filled in 4! ways. So in this case required numbers are 4 × 4! ways.

So, total number of numbers = 120 + 96 = 216

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