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  4. The remainder obtained when 64 × 65 × 66 is divided by 67, is

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Q. The remainder obtained when $64 \times 65 \times 66$ is divided by $67$, is

Permutations and Combinations

Solution:

$64 \equiv - 3$ Mod $(67)$
$65 \equiv - 2$ Mod $(67) ; 66 = - 1$ Mod $(67)$
$\therefore 64 \times 65 \times 66 = (- 3)(- 2)(- 1)$ Mod $(67)$
$= - 6$ Mod ($67) = 61$ Mod $(67)$
$\therefore $ Required remainder is $61$.