A software engineer creates a LAN game where an 8 digit code made up of 1, 2,…
2025
A software engineer creates a LAN game where an 8 digit code made up of 1, 2, 3, 4, 5, 6, 7, 8 has to be decided on as a universal code. There is a condition that each number has to be used and no number can be repeated. What is the probability that the first 4 digits of the code are even number?
- A.
1/70
- B.
1/840
- C.
1/8
- D.
1/40320
Attempted by 5 students.
Show answer & explanation
Correct answer: A
Answer: Option A
Explanation:
Given that an 8 digit code is made up of the digits 1, 2, 3, 4, 5, 6, 7, 8 using all without repeating any number.
Total number of possible codes = 8!
(Because 8 numbers can be arranged in 8 positions in 8! ways)
We have to find the probability that the first four digits of the code are even numbers.
Out of the given 8 numbers, exactly 4 are even numbers.
So, these 4 even numbers will occupy the first 4 positions in 4! ways
The remaining 4 odd numbers will occupy the remaining 4 positions (i.e. the last four positions) in 4! ways
To get an 8 digit code both the first 4 positions and the last 4 positions are to be occupied.
Thus, the total number of codes in which the first four digits are even numbers = 4! × 4!
We know that the probability of an event = Number of favourable outcomes / Total number of possible outcomes
Thus, the required probability = Number of codes with the first four digits as even numbers / Total number of possible codes
= (4! X 4!) / 8!= 1/70