SATHEE: Permutations And Combinations Question 299

Permutations And Combinations Question 299

Question: The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is [Kerala (Engg.) 2001]

Options:

A) 120

B) 300

C) 420

D) 20

Show Answer

Answer:

Correct Answer: C

Solution:

The units place can be filled in 4 ways as any one of 0, 2, 4 or 6 can be placed there. The remaining three places can be filled in with remaining 6 digits in $ ^{6}P_3 $ = 120 way. So, total number of ways = 4 × 120 = 480. But, this includes those numbers in which 0 is fixed in extreme left place. Numbers of such numbers $ =3\times {{}^{5}}P_2=3\times 5\times 4=60 $ 0 × × × Fix $ ^{5}P_2 $ ways 3 ways (only 2, 4 or 6) \ Required number of ways = 480 - 60 = 420.

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Permutations And Combinations Question 299

Question: The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is [Kerala (Engg.) 2001]

Options:

Answer:

Solution:

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