Permutation & combination 1

**targetsep08** · 05-20-2009, 02:44 PM

How many four digit numbers that are divisible by 4 can be formed using the digits 0 to 7 if no digit is to occur more than once in each number?

(1) 520 (2) 370 (3) 345 (4) None

**Md. Minuddin** · 05-20-2009, 04:58 PM

Originally Posted by targetsep08

How many four digit numbers that are divisible by 4 can be formed using the digits 0 to 7 if no digit is to occur more than once in each number?

(1) 520 (2) 370 (3) 345 (4) None

I got answer is 240. So is the answer (4) None or what is the official answer???????

Yah the answer is 370. Previously I took as 0-7 total 7 digit where it will be 8 digit.

**givinggmat** · 05-21-2009, 04:27 AM

For a 4 digit num to be div by 4, the last two digits shuld be divisible by 4.
we shall have 14 such combinations.

The remaining digits are 6.

(i) For the combinations which include 0 (there wuld be 4 combinations - 20, 40, 60, 04)-> there are 6 ways to choose the first digit and 5 ways to choose the second digit to make it 4 digit num.

(ii) For the remaining combinations (14-4 = 10)-> there are only 5 ways to choose the first digit (coz 0 would make it 3 digit num) and 5 ways to choose the second digit to make it 4 digit num.

so,
(i) 30*4 = 120
(ii) 25*10 = 250

total = 370

ans . (2)

It took some time to get this answer... is there a way to solve this in 3 to 4 steps..!!??

**rajatmeh** · 05-21-2009, 09:08 AM

I also solved it in the same manner using 14 combinations.
The key is to know that
For a 4 digit num to be div by 4, the last two digits shuld be divisible by 4.

**targetsep08** · 05-21-2009, 02:56 PM

Thanks guys. I was solving using same method but i also included 44 and got 15 combinations, thus wrong answer.

**eexee** · 05-21-2009, 07:12 PM

agree with givinggmat

answer is 370

dunt think there is any better way than this

**stairway2vee** · 05-21-2009, 07:45 PM

I think the time taking part is figuring out that there are 14 combinations. A swifter way to determine this is -

---- 25 (No. of 4's Multiples between 1 - 100)
------4 (08, 28, 48,68 - Nos. containing 8)
------2 (44 & 100 - Repeating digits)
------5 (Multiples of 4 from 80 to 96 - 100 is already accounted for)
--------
----=14

But then, counting the multiples would be a more certain method and less prone to errors.