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

Question Number 116360 by bemath last updated on 03/Oct/20

A five digits number divisible by 3

is to be formed using the number

0, 1, 2, 3, 4 and 5 without repetition

The total number of ways this can

be done is__

Answered by mr W last updated on 03/Oct/20

0 + 1 + 2 + 3 + 4 = 10 ≢ 0 m o d 3

0 + 1 + 2 + 3 + 5 = 11 ≢ 0 m o d 3

0 + 1 + 2 + 4 + 5 = 12 \equiv 0 m o d 3 ✓

0 + 1 + 3 + 4 + 5 = 13 ≢ 0 m o d 3

0 + 2 + 3 + 4 + 5 = 14 ≢ 0 m o d 3

1 + 2 + 3 + 4 + 5 = 15 \equiv 0 m o d 3 ✓

w i t h 0, 1, 2, 4, 5 w e c a n f o r m

4 \times 4 \times 3 \times 2 \times 1 = 96 n u m b e r s

w i t h 1, 2, 3, 4, 5 w e c a n f o r m

5! = 120 n u m b e r s

\Rightarrow t o t a l 96 + 120 = 216 n u m b e r s

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