A software engineer creates a LAN game where an digit code made up of has to be decided on universal code. There is a condition that each number has to be used and no number can be repeated. What is the probability that first digits of the code are even numbers ?
Solve for the required probability:
There are numbers to be filled in the digit code without any repetition.
We know that probability where and are number of favorable outcomes and total number of possible outcomes respectively.
The number of possible arrangements of this are .
Hence, the total number of outcomes
Out of the given numbers exactly numbers are even.
If the first digits are to be occupied by even numbers then the last digits must be occupied by odd numbers.
Now , the ways of arranging even numbers in first digits are
The ways of arranging odd numbers in last digits are
Hence, the favorable number of outcomes
Hence, the probability that first digits of the digit code being even is .