How many no (four digit) can be found using number 1,2,3,4 not exceeding 4321?

Dear Student,

Please find below the solution to the asked query:

We form four digits numbers from ( 1 , 2 , 3 , 4 ) , As :

Thousands place any one from { 1, 2, 3 } = 3 ways   and Rest of the 3 places ( All the 4 ( 1 , 2 , 3 , 4 ) can be places ) = 4³ = 64

Thus total = 3 $\times$ 64 = 192 numbers

ii) 4 at thousands place:

With either 1 or 2 at hundreds place = 1 $\times$ 2 $\times$ 4 $\times$ 4 = 32

With 3 at hundreds place & 1 at tens place = 1 $\times$ 1 $\times$ 1 $\times$ 4 = 4 [4311, 4312, 4313, 4314]

With 3 at hundreds place & 2 at tens place = 1 $\times$ 1 $\times$ 1 $\times$ 1 = 1 [4321]

Rest of the numbers are greater than 432 , So

Total numbers could be formed = 192 + 32 + 4 + 1 = 229                   ( Ans )

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