Question

Juan bought 16 plants to arrange along the border of his garden. How many distinct arrangements can he make if the plants are comprised of 6 tulips, 6 roses, and 4 daisies?

Answer 1

Answer:

Total number of distinct arrangements=1681680

Step-by-step explanation:

We know that when we arrange n items out of which a items are similar,b items are similar such that a+b=n

then the formula for number of arrangements is given by:

$\dfrac{n!}{a!b!}$

Here, total 16 things are to be arranged

out of which 6 are similar(tulips)

other 6 are similar(roses)

and other 4 are similar(daisies)

(Also 6+6+4=16)

Number of arrangements=$\dfrac{16!}{6!6!4!}$

                                         = 1681680

Answer 2

Permutation can be defined as the distinct number of arrangements that is possible and can be made using a given number of items or letters.

The number of distinct arrangements that can be made is 1,681,680 arrangements.

Juan bought 16 plants and he would like to make arrangements that comprise of : 6 tulips, 6 roses, and 4 daisies

This is calculated as:

$\frac{16!}{6! * 6! * 4!}$

= 1,681,680

Therefore, the number of distinct arrangements he can make if the 16 plants are comprised of 6 tulips, 6 roses, and 4 daisies is 1,681,680 arrangements.

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https://brainly.com/question/21942790