HumptyDumpty wrote:

You're right, my luck, my bad.

Pity, apparently I can't understand the case thorough at the moment.

I'd appreciate detailed troubleshooting to the approach, if someone loves combinatorics.

Kudo for you.

Well, I did dig deep into GMAT combinatorics and got really stuck into some questions.

Out of the many solutions, here's one that uses your approach in principle (Sincere thanks to the expert who helped). Have a look:

Solution:Out of the 4 digits, any 2 have to be the same.

Number of ways this is possible:

4C2 = 6.

Consider one case: Tens digit and units digit are the same:

Number of options for the thousands digit = 9. (Any digit 1-9)

Number of options for the hundreds digit = 9. (Any digit 0-9 not yet chosen)

Number of options for the tens digit = 8. (Any digit 0-9 not yet chosen)

Number of options for the units digit = 1. (Must be the same as the tens digit)

To combine the options above, we multiply:

9*9*8*1 = 648.

Other cases:

#ways if the HUNDREDS digit and the UNITS digit are the same (9*9*8*1)

#ways if the THOUSANDS digit and the UNITS digit are the same (9*9*8*1)

#ways if the HUNDREDS digit and the TENS digit are the same (9*9*1*8)

#ways if the THOUSANDS digit and the TENS digit are the same (9*9*1*8)

#ways if the THOUSANDS digit and the HUNDREDS digit are the same (9*1*9*8)

Total #ways =

648*6 = 3888.

Sincerely hope this helps

If this brought a smile to your face, cleared the doubt clouds and made your day then a quick kudos and a big smilie is in place.

Cheers,

Taz

P.S.: It feels great that I'm able to help & share in the same way that others have helped and shared with me.

Cheers to gmatclub. Cheers to bb

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