Question

Can someone please help me with this? PLEASE I'm so confused.

Answer 1

Given:

Total number of flower cuts = 15 different flowers

Number of flowers Jeanine Baker wants to use = 6 flowers

To find:

Total number of ways 6 flowers can be chosen

Steps:

In this question, we need to find the total number of outcomes of choosing 6 random flowers from a total of 15 flowers

Let's give each flowers a letter, so there will be A, B, C, D, E, F, G, H, I, J, K, L, M, N and O.

Now let's find all the outcomes

Outcomes= ABCDEF, ABCDEG, ABCDEH, ABCDEI, ABCDEJ, ABCDEK, ABCDEL, ABCDEM, ABCDEN, ABCDEO.....

This method will take a lot of time so, i am going to use the formula

`No.outcomes = (n!)/(r!(n-r)!)`

Here n = total number of items, and r = number of items chosen

Also the '!' means factorial, or the product of all positive numbers less then or equal to the number, so n! = n * (n-1) * (n-2) ..... * 1

So, now substituting the formula

`No.outcomes = (15!)/(6! * (n-r)!)`

`No.outcomes=(15!)/(6! * 9!)`

`No.outcomes = (15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/(6*5*4*3*2*1*9*8*7*6*5*4*3*2*1)`

`No.outcomes=(15*14*13*12*11*10)/(6*5*4*3*2*1)` (cutting same numbers)

`No.outcomes = (7*13*3*11*10)/(6)` (simplifying)

`No.outcomes = (30030)/(6)`

`No.outcomes=5005`

Therefore, the total number of ways the 6 flowers can be chosen is 5005 ways

Happy to help :)

If u need help in this topic feel free to ask

Answer 2

Answer: 5005

==================================================

Step-by-step explanation:

Let's say we had the slots A,B,C,D,E,F. Each slot represents where a flower would go.

For slot A, we have 15 different flowers to pick from.

Then slot B has 15-1 = 14 choices

C has 15-2 = 13 choices

and so on. We count our way down until we fill up slot F.

The count down looks like this: 15, 14, 13, 12, 11, 10

Multiply out those values: 15*14*13*12*11*10 = 3,603,600

If order mattered, then this represents the number of ways to select 6 flowers from a pool of 15 total.

However, order does not matter in this case. All that matters is the group overall.

For any group of 6 items, we have 6! = 6*5*4*3*2*1 = 720 different arrangements. That means the value 3,603,600 is too large exactly by a factor of 720.

We divide by 720 to get to (3,603,600)/720 = 5005 which is the final answer

It's the number of combinations where we select 6 from a pool of 15.

-------------------------------

As you can guess, you could use the nCr combination formula as an alternative route. Plug in n = 15 and r = 6 like so

`_n C _r = (n!)/(r!*(n-r)!)\\\\_(15) C _(6) = (15!)/(6!*(15-6)!)\\\\_(15) C _(6) = (15!)/(6!*9!)\\\\_(15) C _(6) = (15*14*13*12*11*10*9!)/(6!*9!)\\\\_(15) C _(6) = (15*14*13*12*11*10)/(6!)\\\\_(15) C _(6) = (15*14*13*12*11*10)/(6*5*4*3*2*1)\\\\_(15) C _(6) = (3,603,600)/(720)\\\\_(15) C _(6) = 5005\\\\`

In the third to last step, notice how we have the 15*14*13*12*11*10 up top and 6*5*4*3*2*1 down below.

This value 5005 can be found in Pascal's Triangle. Look in the row that has 1, 15, ... and count out 7 spaces from the left. You should arrive at 5005. However, you'll need a fairly large Pascal's Triangle to use this method.