Question

(1 point)
your candy jar contains 7 starbursts, 9 tootsie rolls, and 8 jolly ranchers (and no other kinds of candy). you randomly select 2 pieces of candy from the jar. what is the probability that they are different kinds?

Explanation:

Step1: Calculate total number of candies

The total number of candies is $7 + 9+8=24$.

Step2: Calculate number of ways to choose 2 candies

The number of ways to choose 2 candies out of 24 is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 24$ and $r=2$. So $C(24,2)=\frac{24!}{2!(24 - 2)!}=\frac{24\times23}{2\times1}=276$.

Step3: Calculate number of ways to choose 2 - different - kind candies

We calculate the number of ways for each pair - type:

• Starburst and Tootsie Roll: $C(7,1)\times C(9,1)=\frac{7!}{1!(7 - 1)!}\times\frac{9!}{1!(9 - 1)!}=7\times9 = 63$.
• Starburst and Jolly Rancher: $C(7,1)\times C(8,1)=\frac{7!}{1!(7 - 1)!}\times\frac{8!}{1!(8 - 1)!}=7\times8 = 56$.
• Tootsie Roll and Jolly Rancher: $C(9,1)\times C(8,1)=\frac{9!}{1!(9 - 1)!}\times\frac{8!}{1!(8 - 1)!}=9\times8 = 72$.

The total number of ways to choose 2 different - kind candies is $63 + 56+72=191$.

Step4: Calculate the probability

The probability $P$ that the two candies are different kinds is $\frac{191}{276}$.

Answer:

$\frac{191}{276}$