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in Permutations by (51.9k points)
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How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 8000, if repetition of digits is not allowed?

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Best answer

The required numbers are greater than 8000.

Therefore, the thousand’s place can be filled with 2 digits: 8 or 9.

Let us assume that four boxes, then in the first box can either be one of the two numbers 8 or 9, therefore there are two possibilities which is 2C1

In the second box, the numbers can be any of the four digits left, therefore the possibility is 4C1

In the third box, the numbers can be any of the three digits left, therefore the possibility is 3C1

In the fourth box, the numbers can be any of the two digits left, therefore the possibility is 2C1

Thus total number of possible outcomes is 2C1 × 4C1 × 3C1 × 2C1 = 2 × 4 × 3 × 2 = 48.

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