+0

# counting question

0
41
4

A phone number has seven digits and cannot begin with a 0.

How many phone numbers contain the sequence 123?

May 1, 2020

#1
+657
+2

Oops just ignore this

May 1, 2020
edited by LuckyDucky  May 1, 2020
#3
+300
+1

w0t? BTW there are 8 options for the first position. I'm not sure I understood the last few lines, but I could be wrong!

CentsLord  May 1, 2020
#2
+300
+1

First, we need to place "123" in the string of 7 digits. There are 5 ways to do that.

Now, we have to place 8 digits in the first digit, at 0 cannot be one. So far, there are 5 * 8 = 40 ways.

Now, we simply have to place digits in the remaining 3 digits. There are 93 = 729 ways to do that.

Therefore, there are 40 * 729 = 29160 phone numbers :D

May 1, 2020
#4
+20914
0

The number could look like this:  123abcd   --->    10 x 10 x 10 x 10  =  10000  ways

or like this:  a123bcd   --->   9 x 10 x 10 x 10  =  9000  ways

[there are only 9 possibilities for a (because 0 can't be used)]

or like this:  ab123cd   --->   9 x 10 x 10 x 10  =  9000  ways

or like this:  abc123d   --->   9 x 10 x 10 x 10  =  9000  ways

or like this:  abcd123   --->   9 x 10 x 10 x 10  =  9000  ways

Adding these together, we get 46000 ways.

May 1, 2020