the digits 3, 4, 5, 6, and 9

[sanju09]

How many even numbers greater than 40,000 may be formed using the digits 3, 4, 5, 6, and 9 if each digit must be used exactly once in each number?
(A) 36
(B) 48
(C) 64
(D) 96
(E) 112

[krishnakumar.ks]

First digit can have only 4 numbers (4,5,6 and 9)
Second digit can have any of the numbers from the list except the first digit. Hence it can take 4 numbers
Similarly, third, fourth and fifth digits can take 3,2 and 1 numbers respectively.

Hence total number of numbers that can formed using the digits and greater than 40000 is (4*4*3*2*1)= 96

[Anurag@Gurome]

How many even numbers greater than 40,000 may be formed using the digits 3, 4, 5, 6, and 9 if each digit must be used exactly once in each number?

Let us calculate the possible number of integers in each of the following cases,

• 1. The number starts with 5 or 9
  Leftmost place can be filled with either 5 or 9 --> 2
  Rightmost place can be filled with either 4 or 6 --> 2
  Middle 3 places can be filled with any of the rest three integers --> 3! = 6
  
  Hence, a total of 2*2*6 = 24 numbers are possible.
  
  2. The number starts with 4 or 6
  Leftmost place can be filled with either 4 or 6 --> 2
  Rightmost place can be filled with 4 or 6 which was not used in the leftmost place --> 1
  Middle 3 places can be filled with any of the rest three integers --> 3! = 6
  
  Hence, a total of 2*1*6 = 12 numbers are possible.

Hence, a total of (12 + 24) = 36 numbers are possible.

The correct answer is A.

[sanju09]

The correct answer is [spoiler](A)[/spoiler]. The last digit may only be filled by 4 or 6, thus in 2 ways. This leaves 3 remaining numbers for the first digit, 3 more for the second digit, 2 for the third digit and 1 for the fourth digit. 3 · 3 · 2 · 1 · 2 = [spoiler]36[/spoiler].

[zooki]

4 or 6 has to be the last digit for the number to be even. and the integers have to be greater than 40000. i. e. for the 1st digit we have 3 digit after picking 4 or 6 as last digit.

3*_ _ _ *2

for the 2nd digit we have 3, {5/9}, {4/6}

i e. 3*3* _ *_ *2

following the similar manner we have: 3*3*2*1*2= 36