+0

# Question about dots

+1
1218
15

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)

Nov 24, 2018

### 15+0 Answers

#1
+5

Here's my best attempt, tanmai....

o       o         o         o

o      o         o          o

o      o         o          o

o      o         o          o

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   Nov 24, 2018
#2
+2

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.

tanmai79  Nov 24, 2018
#3
+2

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.

tertre  Nov 24, 2018
#4
+2

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.

tertre  Nov 24, 2018
#5
+1

So is there, like, a formula or something to compute that?

tanmai79  Nov 24, 2018
#6
+1

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!

tertre  Nov 24, 2018
#10
+2

I do take AoPS, but it's only the beginning of the year. Counting and Probability is the last 10 weeks of class.

tanmai79  Nov 24, 2018
#11
0

https://web2.0calc.com/questions/strange-q#r5

I thought you know what n choose k means

Guest Nov 24, 2018
#12
0

wait, why is this downvoted? I thought he knew what n choose k means because he used it before Guest Nov 24, 2018
#13
+1

I just don't understand it well.

tanmai79  Nov 24, 2018
#14
0

why are you downvoting me tho

Guest Nov 24, 2018
#15
+1

It's not me downvoting you. Which Guest are you, Guest #1, Guest #2, or a guest I haven't met yet?

tanmai79  Nov 24, 2018
#7
+2

Thanks, tertre     [ and tanmai ]   !!!   Nov 24, 2018
edited by CPhill  Nov 24, 2018
#8
+2

Thank you, CPhill, for providing a wonderful solution! I was actually stumped at first..

tertre  Nov 24, 2018
#9
+1

I just got lucky.....LOL!!!!   CPhill  Nov 24, 2018