Question 1028530
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There are 20 people in a room, and each of the 20 writes down an integer at random from 1-100 inclusive. Find the probability that at least two people wrote down the same number. Express your answer as a decimal rounded to four significant digits.

This is not so complicated; however, how do I "determine the probability of AT LEAST TWO PEOPLE" drawing the same number?

Thank you in advance!!

By the way, the answer is 0.8696
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1.  The full set of outputs is the set of all functions defined on 20 points and taking 100 values. The cardinality of this set is N = {{{100^20}}}.

2.  In how many ways can 20 people write 20 different numbers?

    Take {{{C[100]^20}}} and multiply by 20!: you will get the number of ways

    M = 100*99*98* . . . *82*81.

3. Now the probability under the question is

    {{{1 - M/N}}}.

   It is the same as this number {{{1 - (100/100)*(99/100)*(98/100)* ellipsis *(81/100)}}}.
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