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How many different 4 digit numbers can be composed of digits

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How many different 4 digit numbers can be composed of digits [#permalink] New post 23 May 2007, 00:23
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How many different 4 digit numbers can be composed of digits 0,2 and 3?

A. 48
B. 54
C. 64
D. 72
E. 81
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 [#permalink] New post 23 May 2007, 01:32
to form a 4 digits number out of 0,2,3 we have 54 possible ways:

The first place can only be 2,3 !

the second, third, forth place can be 0,2,3

firstly = 2 (for the first number i.e 2,3)*3! (all the others) = 12

In addition we can have 2,2,2 & 3,3,3 & 0,0,0 as second, third and forth place.

so 2*3 = 6

finally thare are 0,2,2 & 0,3,3 & 3,2,2 & 3,0,0 & 2,3,3 & 2,0,0

total = 2 (for 2,3) *6 (arrangements) *3 (ways to arrange i.e 0,2,2 & 2,0,2 & 2,2,0)= 36

----------------------

total = 36+6+12 = 54

:-D
  [#permalink] 23 May 2007, 01:32
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