Acroissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. how many ways are there to choose a) a dozen croissants? b) three dozen croissants? c) two dozen croissants with at least two of each kind? d) two dozen croissants with no more than two broccoli croissants? e) two dozen croissants with at least five chocolate croissants and at least three almond croissants? f) two dozen croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants?

a) 110,880

b) 8.61x10^37

c) 7.18x10^19

Step-by-step explanation:

To find the amount of options, use the following combination equation.

n!/[r! * (n - r)]

In this equation, n represents the amount of possible options and r represents the amount being chosen at a time. We can now calculate out the answer for each possibility.

a) In this case, n would equal 12 and r would equal 6.

n!/[r! * (n - r)]

12!/[6! * (12 - 6)]

479001600/[720*6]

479001600/4320

110,880

b) In this case, n would equal 36 and r would equal 6

n!/[r! * (n - r)]

36!/[6! * (12 - 6)]

3.72x10^41/[720*6]

3.72x10^41/4320

8.61x10^37

c) For this one, n would equal 24 and r would equal 6. We would also then have to divide the answer at the end by 2.

n!/[r! * (n - r)]

12!/[6! * (12 - 6)]

6.20x10^23/[720*6]

6.20x10^23/4320

1.44x10^20 ÷ 2 = 7.18x10^19

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.