many diffeent arrangments can

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you have a sample of 9 flowers from pea plants. suppose 6 of them are white and 3 of thema re purple. If you line them up in a row,hoow many diffeent arrangments can you get?

now suppose 3 of them are white and 6 of them are purple. How many different arrangments can you get? does this make sense?

How many arrangments do you have for 1 white and 8 purple 

how many arrangements do yo uhave for 0 white and 9 purple

Expert Solution
Step 1

You have a sample of 9 flowers. 6 of them are white and 3 of them are purple.

The formula of getting the number of different arrangement is - 

nCn!r! * (n-r)!

Here, 

n = 9

r = 6

(n-r) = 3

Number of arrangement =9!6! * 3!

                                       =6! * 7*8*96! * 3*2*1

                                      = (7*3*4)

                                      = 84

So the number of arrangement is 84.

Step 2

Now, 3 of them are white and 6 of them are purple.

Here, 

n=9

r=3

(n-r) =6

Number of arrangement -

= 9!3! * 6!

= 84        [as. 6!*3! = 3!*6! ]

So, the result is same as previous.

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