+157 In this square array of 16 dots, four dots are to be chosen at random. What is the probability that the four dots will be collinear? Express your answer as a common fraction.
(someone put in a picture of a 4 by 4 square of dots here)
+129907 Here's my best attempt, tanmai....
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We have C(16, 4) = 1820 possible sets of any four of the points
But.....the only ones that will be collinear points are the four horizontal and vertical patterns and the two diagonal patterns = 10 total
So....the probability is 10 / 1820 = 1 / 182
+157 You got it right!
I've got another question, though:
\(${16 \choose 4}$\)
What does that mean? There is no line to symbolize that it is a fraction.
+4622 It's not a fraction. However, it means 16 choose 4; it computes the number of ways to choose items from a collection of items.
+4622 Also, a quote from CPhill's explanation: "We have C(16, 4) = 1820 possible sets of any four of the points."
We can express this as \(C\binom{16}{3}\) , where it is combinations.
+4622 Oh yes, there is! Here: \(\frac{n!}{r!(n-r)!}\)- combinations; order does not matter
The order does matter( Permutations): \(\frac{n!}{(n-r)!}\)
If you take AoPS, they give you wonderful examples!
+157 I do take AoPS, but it's only the beginning of the year. Counting and Probability is the last 10 weeks of class.
https://web2.0calc.com/questions/strange-q#r5
I thought you know what n choose k means
