Melody

I am just joining some of the sticky notes together :)

This is some interest questions dated 26th sept 2016

Thanks guest, probability is always tricky.

Matleena chooses three numbers at random from the numbers 1, 2, 3,..., 10. What is the probability that they are not all consecutive? (For example, the three numbers 6, 7, 8 are consecutive.)

If the order they are drawn counts then

Number of possible permutations is 10*9*8 and the number of consecutive combinations is 8 

so the probability that they ARE consceutive is  8/(8*9*10) = 1/90

and the probability that they are NOT consecutive is 89/90

If the order they are draw does NOT count then  234 is the same as 324 and this is different

Number of possible combinations is 10C3 = 120

The number of consecutive combinations is still 8

So the prob of getting three consecutive numbers is 8/120 = 1/15

The probability that they are not consecutive is 14/15

WOW Omi, that was an epic effort.

thanks :)

Thanks :)

Looks good to me :)

What is the greatest common divisor of all of the members of the set containing all numbers that are the product of four consecutive positive integers?

With any four consecutive numbers there will always be 2 even ones and one of those will be divisable by 4.

So that means that 8 will always be a factor of their product.

Also there will always be one that is divisable by 3 so there is another common factor.

So 24 will be a common factor.

Now the smallest member of the set is  1*2*3*4= 24

So 24 is the greatest common factor.

That is interesting Hectictar.

I know it is Heureka's formula but I don't remember seeing it before.  

The multiples of 25 are 25,50,75,100 etc

You forgot the 1 times multiples :)

Thanks for haveing a go and it is just a oversight error anyway. :)

Maybe it is, maybe it isn't,  but you have expressed yourself very rudely and unproductively.

If you believe it to be wrong you should be polite, thank the answerer for his/her efforts, and express why you think the answer is incorrect.