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How many 4 digits even numbers are possible from digits 1 to 9 if repetition is not allowed?(a) 6561(b) 2016(c) 1344(d) 2916This question was posed to me in an online quiz.My doubt stems from Fundamental Principle of Counting in chapter Permutations and Combinations of Mathematics – Class 11

Answer»

Correct answer is (c) 1344

Explanation: Total digits are 1-9 i.e.9. Even NUMBER means 2,4,6,8 at unit’s place.

So, 4 possible digits for unit place, after a digit is placed at unit place 8 digits are remaining.

8 ways to fill 1st POSITION, 7 ways to fill 2nd position, 6 ways to fill th3 3rd position.

Hence, by the fundamental principle of COUNTING, total possible numbers are 8*7*6*4 = 1344.



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