Using the digit 2,3,4,5,6 without repition. How many

a) numbers greater than 40000 can be formed?

b) even numbers greater than 40000 can be formed?

c) odd numbers greater than 40000 can be formed?

Guest Oct 1, 2017

#1**+2 **

Using the digit 2,3,4,5,6 without repition. How many

a) numbers greater than 40000 can be formed?

the first digit can be 4, 5, or 6 and the others can be any. So that is

3*4*3*2*1 = 72 ways

b) even numbers greater than 40000 can be formed?

The last can be 2 or 4 or 6 and the first can be 4 or 5 or 6

If the last on is 4 or 6 then there is 2*2*3*2*1 = 24

If the last digit is 2 then there is 1*3*3*2*1 = 18

You have to add those two result together to get the total number. 42 ways

c) odd numbers greater than 40000 can be formed?

The last can be 3 or 5 and the first can be 4 or 5 or 6

If the last on is 3 then there is 1*3*3*2*1 = 18

If the last digit is 5 then there is 1*2*3*2*1 = 12

You have to add those two result together to get the total number. 30 ways

Accept my answer, or anyone elses, at your own peril.

Melody
Oct 1, 2017

#2**+1 **

LOL!!!!!

Doesn't * every* poster have to accept our answers at their own peril ????

CPhill
Oct 1, 2017

#3**+1 **

When the number begins with 4, then there are 4! =24 permutations for 2, 3, 5, 6

Half of them, or 12 would be even, and the other half or 12, odd.

When the number begins with 5, then there are 4! =24 permutations for 2, 3, 4, 6

3/4 x 24 =18 would be even, and 1/4 x 24 =6 would be odd.

When the number begins with 6, then there are 4! = 24 permutations for 2, 3, 4, 5

Half of them or 12 would be even, and the other half or 12 would be odd.

**So, 24+24+24 =72** numbers over 40,000, and:

**12+18+12 =42** would be even, and:

**12 + 6+ 12=30** would be odd.

**Just as Melody found !!**

Guest Oct 1, 2017

edited by
Guest
Oct 1, 2017