CSMC 2018 Part A Problem 3

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High School Math Grades 9-12, Ages 13-18

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CSMC 2018 Part A Problem 3

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#1 h Nov 24, 2018, 5:58 PM • 2 Y

Y by Adventure10, Mango247

A jar contains 6 crayons, of which 3 are red, 2 are blue, and 1 is green. Jakob reaches into the jar and randomly removes 2 of the crayons. What is the probability that both of these crayons are red?

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#2 h Nov 24, 2018, 6:06 PM • 2 Y

Y by Adventure10, Mango247

There are $\binom{6}{2}=15$ ways to choose Any $2$ crayons. There are $3$ ways to choose $2$ red crayons (call them $r_1, r_2, r_3$ , then $(r_1,r_2)$ , $(r_2,r_3)$ and $(r_1,r_3)$ are the ways). So the answer is $\frac{3}{15}=\frac{1}{5}$ .

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