A five-digits number is formed by using the digits 1,2,3,4,5 with no repetition. The probability that the numbers 1 and 5 are always together, is

Step-by-step solution

The total number of ways to form a five-digit number using the digits 1, 2, 3, 4, 5 without repetition is 5! = 120 . To find the number of ways where 1 and 5 are always together, treat the pair (1, 5) as a single unit. This leaves us with 4 units: 1, 5 , 2, 3, 4 . The number of ways to arrange these 4 units is 4! = 24 . Within the unit 1, 5 , the digits 1 and 5 can be arranged in 2! = 2 ways (either 15 or 51 ). Therefore, the total number of favorable arrangements is 4! 2! = 24 2 = 48 . The probability is the ratio