- #1

thenewsteven

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## Homework Statement

A number is chosen at random between 0 and 1. What is the probability that exactly 5 of its first 10 decimal places consists of digits less than 5?

## Homework Equations

Binomial Coefficient = [itex]\displaystyle \binom{N}{n1}[/itex]

Where n1 denotes "n1" objects of an indistinguishable type.

## The Attempt at a Solution

Obviously, 5 digits of the first 10 decimal places of this "number" is less than 5 and the rest are of course greater than 5. Therefore the probability should be [itex]\frac{10!}{10^{10}}.

[/itex]

The authors solution assumes that there are distinct combinations, and the binomial coefficient (combinations) must be used. In fact his answer is [itex]\displaystyle \binom{10}{5}(1/2)^5(1/2)^5[/itex].

I do not agree that there are (10 choose 5) choices for the total number of distinct choices. What is the author's question really asking???