Q. How many 5-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5?	Choose the correct choice from the following answers:
A) 180
B) 120
C) 210
D) 270
E) 300
the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2   i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _   case 1 &gt; 1 _ _ _ _ _ _ here the units digit can be either 2 or 6   when the units digit is 2 i.e 1 _ _ _ _ _ 2   number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60   when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30   case 2 &gt; 2 _ _ _ _ _ _ (here units digit may be 2 or 6)   number of ways this can be done would be 5! / (2!) for 2 =60   and 5! / 2! for 6 ... = 60   adding all of these ... gives the answer 120 ...   the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat   120
<result>B</result>
Q. How many 5-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5?