# Thread: **urgent: Desperate Probability Question**

1. ## **urgent: Desperate Probability Question**

I need to find a generalized equation for this problem:

Given the digits 1, 3, 6 and 9, find the probability that a 4-digit number is formed by using each of them only once and is divisible 7.

I found that there are 24 numbers and 4 are divisible by 7 for those specific digits but when I go to generalize this (and attempt to write an equation) I am lost. I did this via a tree diagram but cannot solve to get a general equation, ie, if 4 random digits are picked, and arranged to make a 4 digit number, what is the probabilty that they are divisible by 7 (there has to be an equation where you can plug in 4 numbers and do get the probability)?

I am lost and need help desperately as this is due in a few days. A push in the right direction PLZ!! thnx!!

2. Assuming they're the only digits that can make up a number...

The probability of them being used once is 4!/4^4 = 3/32

So if 4 are divisible by 7, then it's 4/4^4 = 1/64

3. Is it just the first part of the question that says you use those numbers? Can the general part use all the digits 0 to 9?

If so, then 9999/7 = 1428.4

So there are 1428 numbers from 0 to 9999 divisible by 7

1428/10000 = 357/2500