Questions on combin and permut

[Guest]

In a lotto game, 21 balls gets picked up from a pot of 80 balls.

Scenario 1

If I create all possible combinations of 80 numbers, I get 3160 combinations
[=COMBIN(80,2)].
If I create all possible combinations of 21 numbers (the ones that gets
picked up), I get 210 combinations [=COMBIN(21,2)].

That means if I look at combinations, 210 combinations clicks in one draw
out of 3160.

Scenario 2

There are in all 3160 combinations of 2 numbers. If I check both the numbers
individually, there are chances that both the numbers in a combination of 2
will be present in the draw of 21 numbers or there could be only 1 out of the
2 numbers in a combination that will be present in the draw of 21. The above
scenario says that there are 210 combinations that matches 2 on 2 and an
analysis that I did manually, it says there are 1239 combinations that
matches 1 on 2. Can we come to this figure (1239) using any formula?

Scenario 3

Similary, if I check both the numbers individually, there could be chances
that both the numbers did not fall in the draw of 21 numbers. These are 1711
combinations. Again, Can we come to this figure (1711) using any formula?


I need a formula for calcuating 1 on 2 (scenario2) and 0 on 2 (scenario3)

2:2 =COMBIN(21,2) = 210
1:2 NEED FORMULA = 1239
0:2 NEED FORMULA = 1711

 

[Bernie Deitrick]

Mac,

2) 21 numbers chosen, 59 not chosen, so each could be paired with any, for a
total of

=21*59

or the 1239 that you calc'd.

3) 59 numbers not chosen, means:

=COMBIN(59,2)

will give the 1711

HTH,
Bernie
MS Excel MVP

 

[Guest]

Kewl,

Never thought of the other way round.

Thanx
Maxi

Mac,

2) 21 numbers chosen, 59 not chosen, so each could be paired with any, for a
total of

=21*59

or the 1239 that you calc'd.

3) 59 numbers not chosen, means:

=COMBIN(59,2)

will give the 1711

HTH,
Bernie
MS Excel MVP

In a lotto game, 21 balls gets picked up from a pot of 80 balls.

Scenario 1

If I create all possible combinations of 80 numbers, I get 3160 combinations
[=COMBIN(80,2)].
If I create all possible combinations of 21 numbers (the ones that gets
picked up), I get 210 combinations [=COMBIN(21,2)].

That means if I look at combinations, 210 combinations clicks in one draw
out of 3160.

Scenario 2

There are in all 3160 combinations of 2 numbers. If I check both the numbers
individually, there are chances that both the numbers in a combination of 2
will be present in the draw of 21 numbers or there could be only 1 out of the
2 numbers in a combination that will be present in the draw of 21. The above
scenario says that there are 210 combinations that matches 2 on 2 and an
analysis that I did manually, it says there are 1239 combinations that
matches 1 on 2. Can we come to this figure (1239) using any formula?

Scenario 3

Similary, if I check both the numbers individually, there could be chances
that both the numbers did not fall in the draw of 21 numbers. These are 1711
combinations. Again, Can we come to this figure (1711) using any formula?


I need a formula for calcuating 1 on 2 (scenario2) and 0 on 2 (scenario3)

2:2 =COMBIN(21,2) = 210
1:2 NEED FORMULA = 1239
0:2 NEED FORMULA = 1711

 

[Guest]

Confused again.......

I am clear on the combinations of 2 numbers. If we have to do the same thing
with combinations of 3 numbers then?

Can you please replace all the "?" with data?

0 =COMBIN(59,2) 1711
1 =21*59 1239
2 =COMBIN(21,2) 210
------------------------------------------------------
TOTAL (=COMBIN(80,2) 3160
------------------------------------------------------

0 ? ?
1 ? ?
2 ? ?
3 =COMBIN(21,3) 1330

 

[Bernie Deitrick]

Mac,

=COMBIN(59,3)
=21*COMBIN(59,2)
=59*COMBIN(21,2)
=COMBIN(21,3)
=COMBIN(80,3)

HTH,
Bernie
MS Excel MVP

 

[Bernie Deitrick]

Mac,

Generalizing:

0: =COMBIN(21,0)*COMBIN(59,3)
1: =COMBIN(21,1)*COMBIN(59,2)
2: =COMBIN(21,2)*COMBIN(59,1)
3: =COMBIN(21,3)*COMBIN(59,0)

Starting to see the pattern?

HTH,
Bernie
MS Excel MVP