If four digit numbers are formed by using the digits 1,2,3,4,5,6,7 without repetition, then out of these numbers, the numbers exactly divisible by 25 are

Step-by-step solution

For a four-digit number formed from the digits 1,2,3,4,5,6,7 to be divisible by 25, its last two digits must form a number divisible by 25. The possible two-digit endings are 25 and 75 , as 00 and 50 are not feasible without the digit 0 . Case ending in 25: The digits 2 and 5 are used, leaving 1,3,4,6,7 for the first two positions. There are 5 4 = 20 arrangements. Case ending in 75: The digits 7 and 5 are used, leaving 1,2,3,4,6 for the first two positions. There are 5 4 = 20 arrangements. Total numbers: 20 + 20 =