q28

[Saumyojit]

the latest registration number issued by the delhi motor vehicle registration authority is DL-5S-2234.if all the numbers and alphabets before this have been used up then find how many vehicles have a registration number starting with DL-5


First case: DL-5 A to R --> 18c1 *(10 ^4) = 1,80,000

Another Case -> DL-5S0 --> 10 ^3 =1000

Second Case : DL-5S1 -- > 1000

Third case --> DL-5S21 --> 100


Fourth case : DL-5S22 : 2c1 *10c1

Fifth : Dl-5S223 --> 5 ways

Adding them gives 1,82,125 but ans is 1,82,216

 

[Saumyojit]

Another case --> DL-5S20 --> 100 so 1,82, 225

4th case Correction : DL-5S22 : 3c1 *10c1 (0,1,2)

 

[Saumyojit]

Newly done :

First case: DL-5 A to R --> 18c1 *(9999) = 179982 (0000 EXCluded)

Another Case -> DL-5S0 _ _ _ --> 10 ^3 =999 (0000 EXCluded)

Second Case : DL-5S1 _ _ _ -- > 1000

Third case --> DL-5S21 _ _ --> 100


Fourth case : DL-5S22 _ _ : 3c1 *10c1 = 30

Another case --> DL-5S20 _ _ --> 100

Fifth : Dl-5S223 _ --> 5 ways

Adding them gives 182216

 

[Dr.Peterson]

the latest registration number issued by the delhi motor vehicle registration authority is DL-5S-2234.if all the numbers and alphabets before this have been used up then find how many vehicles have a registration number starting with DL-5

A quicker way:

Starting with A through R, followed by 0000 through 9999: 18*10,000 = 180,000.​

Starting with S, followed by 0000 through 2234 = 2235.​

Total: 180,000 + 2235 = 182,235.​

Am I to assume that 0000 is not allowed, though the problem doesn't say that? Then it's a bad problem (yet again). It explicitly says that all numbers are used.

(The correct word is "letters", not "alphabets". I find this to be a common error in India; so common, in fact, that it can be considered a feature of Indian English. But it's worth knowing that outside India, it looks like a foolish mistake. In light of this, I have to ask: Is "number" defined in India to exclude 0?)