The number of all possible three digit even numbers which can be formed with the condition that if 5 is one of the digits, then 7 is the next digit is equal to

Step-by-step solution

If 5 is at hundreds place, 7 will be at tens place and ones place will have 0,2 , 4,6 or 8 . So, 5 numbers are possible. If 5 is at tens place then, 7 will be at ones place but it won’t be an even number. If 5 is at ones place, then it won’t be an even number. So, 5 can only be at hundreds place 5 _ 7 _ x _ → x = 0,2 , 4,6 , 8 → 5 numbers 8 _ × 9 _ × 5 _ = 360 numbers (any number except 0,5 at hundreds place, any number except 5 at tens place and 0,2 , 4,6 , 8 at ones place) Total numbers possible = 5 + 360 = 365