钥匙题求助！！！！

khe01

两道八月机经都是关于钥匙题的，能帮忙简单说下思路吗？多谢。

1。2钥匙放入5个钥匙的钥匙环中,排在一起的概率
ANSWER 2C(5,1)/P(6,2)  （为什么是P(6,2) 呀？）
2。 put two different keys into a circle of 5 keys. how many the combination could be.
[em24][em24][em27][em27]

redpot

First, because it is a key circle.  There are 6 spaces between those 5 keys.  So, it is P(6,2).
Second, it might be P(7,7)/C(7,7)=P(6,6).

khe01

sorry,  i still cannot understand it. What does the key circle look like? Can you explain it more? thanks a lot.

tongxun

1\ put one key into the circle first, there are 5 posotions; the next one have 6 positions to be put into.then the composition:5*6=30.
2\ two key be combined---p2,2. put these two keys together into 5 positions, so 2*5/30=1/3
do not think such kind question be too difficult.

redpot

yeah.  thanks tongxun.  Actually i made a mistake.  Because it is a circle, actually it has only 5 space.  however, you are going to put 2 keys into it, so you can consider it as 6 spaces for 2 keys.  Or like what tongxun said, C(5,1)*C(6,1)