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Asked Sep 17, 2019
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Assume that 4 digits are selected at a random from the set { 1,2,3,4} and are arranged in random order.

Question: What is the probability that the resulting 4-digit number is less than 8000

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Expert Answer

Step 1

The set of the digits from which the digits are selected randomly and arranged in random order is

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{1,2,3,4

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Step 2

For a four digit number less than 8000, the digit at first place must be less than 8.

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Thus, there are 4 choices for the first place; simultaneously, there are 3 choices for the second place, there are 2 choices for the third place and there is only 1 choice for the fourth place

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Step 3

Thus,

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The favorable outcomes are 4-3-2-1 24 and the total outcomes for a four digit number are also 4-3.2-1 24 That is, for the set of digits 1, 2,3,4}, the digit that is selected randomly and arranged in random order without the condition of"less than 8000" or with the condition of "less than 8000" is same.

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