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How many numbers greater than 2300 can be formed using digits from 0,1,2,3,4,5,6 provided no digit is to be repeated ?

How many numbers greater than 2300 can be formed using digits from 0,1,2,3,4,5,6 provided no digit is to be repeated ?

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Given that the number should be greater than 2300 and the number of digits is four.
Therefore, the numbers with 3,4,5,6 in thousands place will be greater than 2.
But if the number in thousands place is 2, then there is a restriction in hundreds place to make the number greater than 2.
Let us consider two cases.
Case 1:
When 2 occurs at thousands place:
 
The thousands place can be filled up by 2 in 1 way
The hundreds place can be filled up by any of the numbers 3,4,5,6 in 4 ways.
So the remaining two places can be filledup in 5P2 ways.
Therefore the total numbers formed inthis case = 1 x 4 x 5P2 = 80
Case 2:
When 3,4,5, or 6 occurs at thousands place.
The thousands place can be filled in 4 different ways
So the remaining three places can be filledup in 6P3 ways.
Therefore the total numbers formed inthis case = 4 x 6P3 = 480
 
Therefore, the required number = 80 +480 = 560

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