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 September 17th, 2018, 08:12 AM #1 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 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? September 17th, 2018, 09:07 AM #2 Senior Member   Joined: Feb 2010 Posts: 711 Thanks: 147 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 Tags 5digit, combinations, created, number Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Shen Elementary Math 3 June 6th, 2014 12:27 AM Shen Elementary Math 2 June 5th, 2014 07:50 AM life24 Number Theory 8 February 20th, 2014 10:16 AM life24 Advanced Statistics 2 February 17th, 2014 04:24 AM sachinrajsharma Number Theory 7 April 29th, 2013 05:49 AM

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