Question

How many 4 digit numbers are divisible by 5 can be formed with digits 0,1,2,3,4,5,6 and 6?

Answer 1

Unit digit can be chose in 2 ways- either 0 or 5.

When unit digit is 5:
With just a single 6:

Number of numbers possible = 5 * 5 * 4 = 100 (as  MSD cannot be a 0)

Now, two 6's can come as 66x 6x6 or x66, and this counts to 5 + 5 + 4 = 14 numbers (for the last case, x can only be from 1-4 and not 0)

So, total numbers ending in 5 = 100 + 14 = 114.

When unit digit is 0:
With just a single 6:

Number of numbers possible = 6 * 5 * 4 = 120

Now, two 6's can come as 66x 6x6 or x66, and this counts to 5 + 5 + 5 = 15 numbers.

So, total numbers ending in 0 = 120 + 15 = 135.

Thus, total numbers divisible by 6 = 114 + 135 = 249.

Comments

@arjun sir, you have solved this for non-repeating case but how to get know about for which case we have to solve the question, repeating or non-repeating?

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It should be specified in question. In this question two 6's is a hint that digits cannot be repeated.

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why cant we just find total numbers can be formed by using these digits then divide the numbers by 5 to get numbers divisible by 5. total 4 digits numbers can be formed using these digits are 7*7*6*5=1470 dividing by 5 gives 294 as answer.> plz clarify