SOLUTION: Hi, could you please advise where to start on the following question... How many different ways can a gardener who has five (identical) red flowers, 3 (identical) pink flowers a

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Question 477739: Hi, could you please advise where to start on the following question...
How many different ways can a gardener who has five (identical) red flowers, 3 (identical) pink flowers and 2 (identical) white flowers plant all the flowers in a row?
Thanks in advance
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i believe the combination formula will give you your answer.
you have 5 red flowers, 3 pink flowers, and 2 white flowers.
i believe you answer will be given by the following formula:
number of possible combination is equal to:
n!/(x!*y!*z!)
n is the total number of flowers
x is the number of red flowers
y is the number of pink flowers
z is the number of white flowers
the actual numbers replace the letters to get:
10!/(5!*3!*2!) which is equal to 2520 possible arrangements.
this is hard to see because there are so many combinations.
it's easier to see when there are fewer.
assume you had 5 flowers in total.
2 are red and 3 are blue
the number of ways you can arrange them should be 5!/(2!*3!) = 10
if we let a equal to the red flowers and b equal the blue flowers, then we can model the arrangements are shown below:
aa is in the first 2 positions
aabbb
ab is in the first 2 positions
ababb
abbab
abbba
ba is in the first 2 positions
baabb
babab
babba
bb is in the first 2 positions
bbaab
bbaba
bbbaa
total possible combinations is 10.
same concept works with the bigger numbers.
10! / (5!*3!*2!) = 2520 possible arrangements.