HOW TO CALCULATE THE NUMBER OF VARIATIONS IN A 4-DIGIT NUMBER

Start by writing down all the possibilities for the first digit. They are
0
1
2
Use each of these as a base for a two digit number. [ From each of the one digit numbers you can construct 3, two digit number, they are
00
01
02
10
11
12
20
21
22
Hence there are 3 3 = 9, two digit numbers.
Use each of these as a base for a three digit number.

From each of the two digit numbers you can construct 3, three digit number, they are
000
001
002
010
011
012
020
021
022
100
101
102
110
111
112
120
121
122
200
201
202
210
211
212
220
221
222
Hence there are 3 3 3 = 27, three digit numbers.
Use each of these as a base for a four digit number. From each of the three digit numbers you can construct 3, four digit number. there are 3 3 3 3 = 81, four digit numbers. ]

Expert answered|cowgirljess|Points 101|

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Asked 3/25/2010 2:51:37 PM

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