You are Here: Home >< Maths

# Calculating the number of times individual digits appear in each combination. watch

1. Good afternoon,

I am trying to work out the total times a particular digit comes out in every combination of a COMBIN(49,6) lottery.

So for example, the digit 0, of which there are 4 (10,20,30,40), will appear...
0 = 8,145,060 combinations where digit 0 appears NO times in the total COMBIN(49,6) combinations.

1 = 4,887,036 combinations where digit 1 appears 4,887,036 times in the total COMBIN(49,6) combinations etc.

2 = 893,970
3 = 56,760
4 = 990
5 = N/A
6 = N/A
7 = N/A

For 0 I used the Excel formula =COMBIN(4,0)*COMBIN(45,6)
For 1 I used the Excel formula =COMBIN(4,1)*COMBIN(45,5)

Now my question is, what formulas do I use for say digit 1, of which there are 14 (1,10,11,12,13,14,15,16,17,18,19 ,21,31,41)

For 0 I used the Excel formula =COMBIN(14,0)*COMBIN(35,6) which worked OK.

I tried the Excel formula =COMBIN(14,1)*COMBIN(35,5) which gave me 4,544,848 which is wrong, it should be 4,220,216, a difference of 324,632.

I think it might be to do with the fact that there is a double digit within the 14 occurances of digit 1, that being 11.

If anyone has any ideas I will be grateful.

2. I think it is 48C5
3. Thanks for the reply, unfortunately this is not the scenario I am looking for.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 24, 2016
Today on TSR

### Edexcel C4 Maths Unofficial Markscheme

Find out how you've done here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams