How many 4digit nymbers with sm of digits equal to 27 are possible. if the digit are not repeated
Answers
Hmm. OK, lets start with the opposite of what is not allowed. We know that it's a 4 digit no and the sum of the digits has to be 28. Also, 4*7 = 28.
Let the no be 7777. However, no repetition is allowed.We try to re-arrange the given digits to form other acceptable 4 digit numbers.
Let's rearrange by reducing the value of the hundreds place by 1,and add it to the tens place : 7687. Again, take 2 units from the hundreds place and add it to the units place : 7489. All the conditions are met. Thus, as there are 4 distinct digits, the total no of arrangements possible: 4! = 24.
Again, lets try to rearrange the given number to see if we can end up with another such unique pair of combination : Reduce the value of the thousands place by 1 and add it to the hundreds place : 6589. Again, unique combination : 4! = 24.
Any other combination of value(s) will result in one of these 48 numbers.
Noteworthy point: The lowest of these numbers can only be of the form : 4XYZ.