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Question

How many numbers greater than $$24,000$$ can be formed by using digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ when no digit is repeated


A
36
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B
60
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C
84
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D
120
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Solution

The correct option is B $$84$$
The digits are 1, 2, 3, 4, 5. We have to form number greater than 24000. Required number will be = (Total) - (Those beginning with 1) - (Those beginning with 21) - (Those beginning with 23)

$$\implies 5!-4!-3!-3!=120-24-6-6$$

Hence the numbers greater than 24,000 that can be formed here = 84

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