Math Is Fun Forum

A secret code that needs to be key-ed in using only 1,2,3,4,5 button. If to open the door, u need to press three buttons, how many possible ways there to open the door? Assume tat the same code may be repeated.

For now, i have to ways in mind...it's either

5 x 5 x 5

OR

1st condition- all numbers are different = 5p3
2nd condition- 2 num r de same, 1 is diff = (3p3/2p2) x 4
3rd condition- all num r de same = (3p3/3p3)

and add all the answers together..

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i'm nt sure which would b a better way..or the correct way..pls help..

Hi guys,

I have a question here which is really causing me headache. Hopefully, someone could help me with this

The positions of nine trees which are to be planted along the sides of a road, five on the north side and four on de south side.

                       O   O   O   O   O     ---North
                     
                         O   O   O   O         ---South

So, the first question is:

Find the number of ways in which this can be done if the trees are all of different species.

ANS: what i have in mind is this... 9P5 x 4! coz first one gotta pick 5 out of the nine to arrange 1st and then the balance will be 4!

next question will be:

If the trees in the above question are planted in random, find the probability that two particular trees are next to each other on the same side of the road.

ANS: the prob I have is that I dunno if i should treat each tree as unique or not. So far, what I have in mind is this:

(4! x 2! x 4!)/(9P5 x 4!) + (3! x 2! x 5!)/(9P5 x 4!)

I'm nt sure if this is right or not...

Pls do correct me if i'm wrong..THANKS A MILLION!!!