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the number of four digit even numbers that can be formed using 0,1,2,3,4,5,6 without repetition is what.

the number of four digit even numbers that can be formed using 0,1,2,3,4,5,6 without repetition is what.

Grade:12

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
For an even number its unit digit should be 0,2,4 or 6 so there are 4 ways.
For a 4 digit number __ __ __ __
6 5 4 4
As it is a 4 digit number 1stnumber shouldnot be zero.so 6 ways
Hence total number of ways=6*5*4*4=480 ways
Thanks and Regards
Shaik Aasif
askIITians faculty
Latika Leekha
askIITians Faculty 165 Points
7 years ago
There can be two cases:
Case (1): When the first digit is even:
We can have the first digit as 2 or 4 or 6 = 3 choices
Similarly, the last digit can be any of 0, 2, 4 or 6 except the first chosen = 3 choices.
Hence, total number of possibilities = 3. 5. 4.3 = 180
Case (2): When the first digit is odd:
We can have the first digit as 1, 3 or 5 = 3 choices
The last digit can be = 0, 2, 4, 6 = 4 choices
Hence, the total number of possibilities = 3.5.4.4. = 240
Hence, the total number of cases = 180 + 240 = 420 ways.
Thanks & Regards
Latika Leekha
askIITians Faculty

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