How many distinct car numbers can be formed using two letters and three digits? The two letters must be distinct and first digit should be non zero?

468000 b] 676000 c] 608400 d] 585000

for ex ap 539

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- Mar 7th 2006, 12:28 AMbharathleceplz solve this
How many distinct car numbers can be formed using two letters and three digits? The two letters must be distinct and first digit should be non zero?

468000 b] 676000 c] 608400 d] 585000

for ex ap 539 - Mar 7th 2006, 01:36 PMThePerfectHackerQuote:

Originally Posted by**bharathlece**

$\displaystyle 26(25)(9)(10)(10)=58500$ - Mar 8th 2006, 02:33 AMRich B.
Greetings:

PHkr's solution would be correct if the two letters and three digits were required to occupy specific positions within the five character succession, e.g., letters followed by digits, letter in first and last position with digits between. Because no such rule of order is specified, we must consider, for instance, that the letters can assume any of 5c2 different configurations (e.g., positions 1 and 2, 1 and 3, etc.). Hence the solution put forth by PHkr need only be modified by a factor of 5c2=10, putting the number of arrangements at 10(26)(25)(9)(10)(10).

Regards,

Rich B. - Mar 8th 2006, 04:19 AMCaptainBlack
[QUOTE=Rich B.]Greetings:

PHkr's solution would be correct if the two letters and three digits were required to occupy specific positions within the five character succession, e.g., letters followed by digits, letter in first and last position with digits between. Because no such rule of order is specified, we must consider, for instance, that the letters can assume any of 5c2 different configurations (e.g., positions 1 and 2, 1 and 3, etc.). Hence the solution put forth by PHkr need only be modified by a factor of 5c2=10, putting the number of arrangements at 10(26)(25)(9)(10)(10).

Which is nice, in that the proposed solution is now one of the

options offered. :)

RonL - Mar 8th 2006, 04:44 AMRich B.Indeed!
Hi Ron:

Indeed! In fact, it was that fact that tipped me off to take a closer look.

Enjoy the day.

...Rich