Question

How many 3 digit numbers have no repeated digits?

Answer 1

wrong. :(

Answer 2

i know...sorry

Answer 3

I think the easiest way would be to figure out how many do have repeated digits, and then take that number away from 900. So look for all the numbers of the form:
XXY
XYX
YXX
For example, an XXY number would be something like 336, or 771. XYX would be like 595, or 424. YXX could be like 766, or 388

Answer 4

ok u have 100
101
110
111
112
113
114
115
116
117
118
119
121
122
131
133
141
144
151
155
161
166
171
177
181
188
191
199
200
202
211
212
.............................................................

idk can't find any f(x) 2 express tht

Answer 5

Oh, also count all the numbers that are XXX.

Answer 6

the answer is 648

Answer 7

till 999 actually

Answer 8

how did u get tht?

Answer 9

i dont know

Answer 10

Til 999, but there are 900 numbers between 100 and 999. I got 647, so I guess I made a calculation error somewhere.

Answer 11

Yep, found my error. I wrote that there were 10 numbers of the form XXX, when there are in fact 9. Silly me! Anywho, did you give it a shot mynameisanon?

Answer 12

This is actually a problem related to permutations.

First you consider the number of ways of arranging 10 objects (0-9) in three positions.
We have: \(10\cdot 9\cdot 8\)
Then you subtract the number three digit permutations with zeros first
We have: \(9\cdot 8\)

The final total is:
\(10\cdot 9 \cdot 8 - 9 \cdot 8 = 648\)

Answer 13

I really think this is what they intended you to do instead of manually counting.

Answer 14

In any case let me know if you have any questions.