find the total number of 4 digit even numbers that can be formed using the numerals 0,1,2,3,5,6 without any repetition

Asked by chaitra k k | 30th Nov, 2013, 09:53: PM

Expert Answer:

There are two cases: The 4th (unit) digit can be 0 or 2.
 
Case1: Let the fourth digit be 0.
 
Therefore, the first digit can be selected in (1,2,3,5,6) 5 diffterent ways.
 
The second digit can be selected in 4 different ways.
 
The third digit can be selected in 3 different ways.
 
Thus the number of 4 digit even number can be formed is .
Case2: Let the fourth digit be 2.
 
Therefore, the first digit can be selected in (1,3,5,6) 4 diffterent ways.
 
The second digit can be selected in 4 different ways.
 
The third digit can be selected in 3 different ways.
 
Thus the number of 4 digit even number can be formed is                                 
Thus the total number of 4 digit even numbers that can be formed is 60 + 48 = 108

Answered by Vimala Ramamurthy | 30th Nov, 2013, 11:20: PM

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