Hi I have stickied this topic because we need a new question thread
I'll be more than happy to help you answer this question and welcome to atarnotes!
Hi, the question is:
A three-digit number is selected from the numbers 3,4,5,7,8,9 with no repetition
What is the probability that he number formed is greater than 800?
Okay lets get started with this! I'll do it from the start just for clarifications sake
We know that anything that starts with a 3,4,5 or 7 will not be bigger than 800. So we can put them aside for now.
834, 835, 837, 839 etc. There are 4 different ways to fill in the third digit.
So for 83? there are 4 possibilities. There are 5 possibilities for 800's (eg 830,840,850)
Thus there are 20 possibilities it can start with an 8. This means that there are also 20 possibilities it can start with a 9. This makes 40 possibilities of it being greater than 800.
But how many possibilities are there? Well there are 20 each for 3, 4, 5, and 7 as well (total 80 possible numbers).
This makes 120 possible numbers. 40 of these are above 800.
Therefore, the possibility is 40/120 or 1/3 (simplifying the fraction).
If I have gone to fast or too slow please tell me so I can adjust my pace. I am currently at the top of my Gen Maths course but am unsure what level you are at. So I just assumed you would want the whole working out.
The short way is 6 x 5 x 4 = 120. (6 ways to fill the 1st number, 5 ways to fill the 2nd number and 4 ways to fill the 3rd number as they are without repetition).
Hope I helped and let me know what method you prefer!