Question 151913: HOW MANY FOUR DIGIT NUMBERS CAN BE FORMED FROM 1,2,3,4,5,6,7 WHICH IS GREATER THAN 3400?
Found 2 solutions by nabla, Levski123:
Answer by nabla(475)   (Show Source):
Answer by Levski123(6) (Show Source):
You can put this solution on YOUR website! Thing of it like this
4 digit number X1 X2 X3 X4 > 3400 so 3401 the lowest possible number greater than 3401. We need to make sure that whatever combination of numbers we make we cannot have a number lower than this. To achieve this we do the following
For X1 there are 5 possible numbers that we can use (3,4,5,6,7, 3 is counts because our lowest acceptable value is 3401 as we determined) for X2, we have 4 possible values (4,5,6,7, again the digit 4 is included, as it its withing our lowest limit. We can't have digit 1 because that means we will accept values like 31XX which is lower than the 3400). With that logic in mind X3 have 7 values, This is because it does not matter what value the X3 digit has as all values are greater than 0 (which is the lowest acceptable digit based on 3401). And finally for the last digit we can have 7 again also because because at this point our lowest possible number so far is 341X which is already bigger than the 3400... So X4 is 7.
No using the fundamental counting principle to add up all the possible combinations we multiply each possible digit combination so X1 x X2 x X3 x X4 = 5x4x7x7 = 980 possible combinations higher than 3400
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