Melody

What is the largest integer n such that 3^n is a factor of 1 x 3 x 5 x... x 97 x 99?

How many of those numbers has a factor of 3

3,6,9, ........99     There are 33 of them

Divide each of these by 3

1,2,3,......  33

Which of these have a factor of 3

3,6,9, ... 33       There are 11 of them

Divide each of these by 3

1,2,3,......  11

Which of these have a factor of 3

3,6,9      There are 3 of them

Divide each of these by 3

1,2,3

Which of these have a factor of 3

3      There are 1 of them

33+11+3+1= 48

I think that the largest n is 48

The interior angles of a convex nonagon have degree measures that are integers in an arithmetic sequence. What is the smallest angle possible in this nonagon?

Can you do any of this for yourself?

For example.  

What is a nonagon?

What is the angle sum of a nonagon?

What is the formula for an arithmetic sum?

Answer these and then I will help more.

No other answerer interfere, thank you.  

A bag contains 4 red marbles, 5 yellow marbles, and 6 blue marbles. Three marbles are to be picked out randomly (without replacement). What is the probability that exactly two of them have the same color?

15 marbles.  Let each one have a unique number, so in this sense, there are all different.

How many combinations are there

All red    4C3=4

All yellow    5C3=10

All blue   6C3=20

All the same colour=34

Exactly 2 red = 4C2*11 = 66

Exactly 2 yellow = 5C2*10=100

Exactly 2 blue = 6C2*9=135

Exactly 2 the same colour = 301

All different = 4*5*6=120

So

P(exactly two of them have the same color) = 301 /(23+301+120) = 301 / 444

(This is my logic, not necessarily correct)

Please put only one question per post.

AND leave out the meaningless $ signs.

To me this looks like the post of a very lazy person who cannot even be bothered presenting his question properly.

Yes, sorry, my mistake.

Yes that is right.

Hi  Madyl,

Try watching this.    

They are made moderators by the operator (owner/developer) of the site.  He is almost never active as a participant, on the forum. 

Thanks guest,

Yes it is a relatively common roadside, in the country anyway. :)

I actually took a photo to use here but I cannot remember if this is my photo or a different one from the internet.