Question

# The number of integers greater than $$6,000$$ that can be formed, using the digits $$3, 5, 6, 7$$ and $$8$$, without repetition, is

A
216
B
192
C
120
D
72

Solution

## The correct option is B $$192$$We can have either $$4$$ digit or $$5$$ digit number.First consider $$4$$ digit number.We can take $$6,7,8$$ at the thousandth place.The next three places can be filled in $$^4{C}_3 \cdot 3!$$ way.So we get $$72$$ such numbersFor $$5$$ digit number, we can choose them in $$5!$$ ways$$(120)$$.So total no of such numbers are $$72+120=192$$.Mathematics

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