All language subtitles for 07 - Calculate combinations with duplication

- [Instructor] In the previous movie,

I described how to calculate the number

of possible combinations that are allowed

from a set of items

when you select a subset.

However, we assumed that duplication was not allowed.

So you couldn't pick two of the same thing.

In this movie,

I will show you how to calculate combinations

where duplication is allowed.

So you can select two or more of the same item.

As an example, if we have a gift basket with three items,

instead of having your employee grab three distinct items

and making sure they're all different,

they could grab anything they wanted.

So they could have two or even three of the same thing.

However, we're dealing with combinations, not permutations.

So the order of the items still doesn't matter.

They'd probably get moved around

in the basket or the gift box anyway.

So how are we going to approach those?

Well, the idea is that we need to determine

how many unique groups are possible

when choosing three of five products

when repetition is allowed.

To demonstrate the process,

I'll switch over to Excel.

I have switched over to this movie's Excel sample file.

It is, 06_07_Combinations With Duplication.

And you can find it

in the chapter six folder of the exercise files collection.

I have also left the calculation

from combinations without duplication

from the previous movie for comparison.

As before, I have the number of available products

in cell B3 and the number of items of a sample basket,

in other words,

the number chosen, in B4.

So I'll click in cell B7,

type an equal sign.

And the function we use

for combinations with duplication is COMBINA.

And this returns the number of combinations

with repetitions allowed for a given number of items.

So I'll make sure COMBINA is highlighted, press tab,

and now we need to identify the number.

That's the number of items available.

So that's in B3.

Type a comma,

and then I'll click B4,

the number chosen,

right parentheses, then enter.

And instead of having 10 combinations without duplications,

if we allow duplication, we have 35.

Now let's see what happens when we increase the number

of available products and the number chosen.

So I'll start in B3 and I'll change the value

from five to eight and press enter.

And we go from 10 and 35

to 56 and 120.

If I allow four items to be selected,

instead of just three out of the eight,

we go from 56 and 120

up to 70 and 330.

And again, the number

of combinations increases more slowly than permutations

because for permutations, order matters.

And for combinations, it doesn't.

But I'm sure you can see

that as we increase the number

of available products and the number of items

in the sample basket,

that combinations both with

and without duplication will increase very quickly.