Question

In how many ways can 5 roses, 6 tulips, and 3 daisies be given to 14 women if each woman receives exactly 1 flower?

Answer 1

theres a counting principle at work here, what would you say it is?

Answer 2

Is it permutations?

Answer 3

almost, im thinking of a more general form of it.

recall what you had to do when say mississippi is used, and you are asked to find the number of ways the you can combine the letters.

Answer 4

11 elements, 4 are the same, 4 are the same, 2 are the same, and 1 is the same

\[\frac{11!}{4!4!2!1!}\]

Answer 5

And then you would do 11*10*9*8*7 ect.?

Answer 6

we have 14 roses to hand out ... 5,6,3 are the same

Answer 7

So 14!/5!6!3!?

Answer 8

thats the memory this setup brings to mind. not saying its correct tho :)

Answer 9

Okay let me calculate

Answer 10

It all checks out at 168,168 thank you

Answer 11

yay!!

Answer 12

in an attempt to justify the process.

aaa bb cc

but just in a's alone there is 3! ways to order it

2! ways in b

2! ways in c

so in this one setup alone we have 3!2!2! duplications

out of the 7! ways to arrange the setup, we have 3!2!2! duplications that need to be factored out.

Answer 13

Makes sense, thanks!