800guy wrote:As a part of a game, four people each much secretly chose an integer between 1 and 4 inclusive. What is the approximate likelihood that all four people will chose different numbers?
this question comes from the difficult math doc on this website, OA coming after some people answer.
The first person can choose any of the four numbers.
P(2nd person chooses a number not yet chosen) = 3/4. (4 total numbers, 3 of them not yet chosen.)
P(3rd person chooses a number not yet chosen) = 2/4. (4 total numbers, 2 of them not yet chosen.)
P(4th person chooses a number not yet chosen) = 1/4. (4 total numbers, 1 of them not yet chosen.)
Since we want all of the events above to happen together, we multiply the fractions:
3/4 * 2/4 * 1/4 = 3/32.
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