Number of 7-digit codes from 1,234,567

Hi Sri,

I'm going to give you a hint and let you try this question again. According to the instructions in this question, you must use each digit ONCE. Think about how that would affect the "math."

GMAT assassins aren't born, they're made,
Rich

Hi Sri,

The prompt tells us that we have to "rearrange" the digits, implying that each digit is used just once. Attention to these types of details matters….

GMAT assassins aren't born, they're made,
Rich

gmattesttaker2 wrote: How many 7-digit codes can be made by rearranging all the digits of the number
1,234,567, if the thousands digit must be odd?

(A) 1,080
(B) 1,440
(C) 2,160
(D) 2,880
(E) 3,120

My approach is the same as some others in that it employs the Fundamental Counting Principle (FCP).
I just to formalize the approach so that people can see why the answer is D

Take the task of arranging the 7 digits and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select the thousands digit
Since this digit must be ODD, we can choose from 1, 3, 5 or 7
So, we can complete stage 1 in 4 ways

Stage 2: Select the units digit
There are 6 remaining digits from which to choose, so we can complete this stage in 6 ways.

Stage 3: Select the tens digit
There are 5 remaining digits from which to choose, so we can complete this stage in 5 ways.

Stage 4: Select the hundreds digit
We can complete this stage in 4 ways.

Stage 5: Select the ten thousands digit
We can complete this stage in 3 ways.

Stage 6: Select the hundred thousands digit
We can complete this stage in 2 ways.

Stage 7: Select the millions digit
We can complete this stage in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 7 stages (and thus arrange all 7 digits) in (4)(6)(5)(4)(3)(2)(1) ways ([spoiler]= 2880 ways[/spoiler])

Answer: D
--------------------------

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent