A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4,5 WITH OUT REPETITIONS .
A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4,5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY5?
Answer/Solution
12/15
Steps/Work
If a number is divisible by 5 the last 1 digits of the number has 5.
If the number ends with 15: Number of possibilities = 4*3 * 2 * 1 = 24
number ends with 25: Possibilities = 4*3 * 2 * 1 = 24
number ends with 35: Possibilities =24
number ends with 45: Possibilities =24
Total number of possibilities with restriction = 24*4= 96
Total number of possibilities without restriction = 5! = 120
Probability = 96/120 = 12/15
Answer: A
If the number ends with 15: Number of possibilities = 4*3 * 2 * 1 = 24
number ends with 25: Possibilities = 4*3 * 2 * 1 = 24
number ends with 35: Possibilities =24
number ends with 45: Possibilities =24
Total number of possibilities with restriction = 24*4= 96
Total number of possibilities without restriction = 5! = 120
Probability = 96/120 = 12/15
Answer: A