Question

A five-digit number divisible by 3 is to be formed using numerals 0,1,2,4,6 and 8 without repetition. The total number of ways this can be done is:
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Answer 1

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$\huge\rm\underline\purple{Question :-}$

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

$\huge\rm\underline\purple{Answer :-}$

Since a five-digit number is formed by using digits 0,1,2,3,4 and 5, divisible by 3 i.e., only possible when the sum of digits is multiple of three which gives two cases.

Case I:

Using digits 0,1,2,4,5 the number of ways =4×4×3×2×1=96.

Case II:

Using digits 1,2,3,4,5 the number of ways =5×4×3×2×1=120

Therefore, total number formed =120+96=216.

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