How many $3$ digit even numbers between can be formed with the digit $0, 1, 2, 3, 4, 5$ and $6$ with no repetition.

105

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57

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51

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None of these

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Solution

The correct option is A $105$

$T h o u s a n d^{'} s p l a c e c a n b e f i l l e d w i t h e i t h e r o f 1, 2, 3, 4, 5, 6 i n 5 w a y s a n d f o r n u m b e r t o b e e v e n u n i t s p l a c e c a n b e f i l l e d w i t h e i t h e r o f 2, 4, 6 i n 3 w a y s a n d t h e h u n d r e d s p l a c e c a n b e f i l l e d w i t h r e m a i n i n g d i g i t s i n 5 w a y s ∴ P e r m u t a t i o n = (5 \times 5 \times 3) + (6 \times 5 \times 1) = 75 + 30 = 105 w a y s$

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