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Answer :
The number of choices the gardener has is 440440
What is a combination?
It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.
The formula for combination is [tex]^nC_r[/tex] = n! / r!(n - r)1
We have,
Number of geranium = 14
Number of lilies = 12
Number of geranium bought = 5
Number of lilies bought = 3
The number of choices.
= [tex]^{14}C_5 \times ^{12}C_3[/tex]
= (14 x 13 x 12 x 11 x 10)/(5 x 4 x 3 x 2) x (12 x 11 x 10)/(3 x 2)
= 14 x 13 x 11 x 2 x 11 x 10
= 440440
Thus,
The number of choices is 440440.
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