My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree1Thanks
  • 1 Post By mrtwhs
Reply
 
LinkBack Thread Tools Display Modes
September 17th, 2018, 08:12 AM   #1
Member
 
Joined: Sep 2014
From: Sweden

Posts: 94
Thanks: 0

Question How many different 5-digit number combinations can be created?

How many different 5-digit number combinations can be created using 5, 7ths and 3, 2s?

77777 | 5
222 | 3


So my first thought was to use this formula:

$\displaystyle n_{1} * n_{2} * ... * n_{n}$

So that I get:
$\displaystyle 5! = 5 * 4 * 3 * 2 * 1$
but this is probably just calculating how
many ways I can put all 7s. And I only
have 7s so it do not tell me much.

Then I would do the same thing for the 3, 2s.
And that can't work. I thought if I added
the two results that might give me the
answer, but I think it doesn't since I only
find out how many combinations it is possible
to put 5, 7s in and 3, 2s in.

So I thought the problem might want me to
use this formula:

$\displaystyle \frac{n!}{(n - k)!}$

So how do you actually begin to solve this?
DecoratorFawn82 is offline  
 
September 17th, 2018, 09:07 AM   #2
Senior Member
 
mrtwhs's Avatar
 
Joined: Feb 2010

Posts: 692
Thanks: 132

You have five 7's and three 2's and wish to construct a five digit number.

One way is to directly count cases
five 7's and zero 2's for a total of $\displaystyle \dfrac{5!}{5!0!}=1$ way
four 7's and one 2 for a total of $\displaystyle \dfrac{5!}{4!1!}=5$ ways
three 7's and two 2's for a total of $\displaystyle \dfrac{5!}{3!2!}=10$ ways
two 7's and three 2's for a total of $\displaystyle \dfrac{5!}{2!3!}=10$ ways

Adding gives $\displaystyle 1+5+10+10=26$ ways.

The only other way I know is to use an exponential generating function. Go look it up.
Thanks from DecoratorFawn82
mrtwhs is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
5digit, combinations, created, number



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
How many three digit number whose digit sum is 13 leave reminder 1 divided by 4 Shen Elementary Math 3 June 6th, 2014 12:27 AM
natural number multiple of another number if its digit sum equal to that number Shen Elementary Math 2 June 5th, 2014 07:50 AM
Four-digit number life24 Number Theory 8 February 20th, 2014 10:16 AM
Four-digit number life24 Advanced Statistics 2 February 17th, 2014 04:24 AM
Number system - proving 9 digit number not divisible by 5 sachinrajsharma Number Theory 7 April 29th, 2013 05:49 AM





Copyright © 2018 My Math Forum. All rights reserved.