At the first tri-city meeting, there were 8 people from town people from town B, and 5 people from town . If the
council consists of 5 people, find the probability of 3 from town A and 2 from town B.

Question

At the first tri-city meeting, there were 8 people from town

people from town B, and 5 people from town

. If the
council consists of 5 people, find the probability of 3 from town A and 2 from town B.

UpStudy AI · Accepted Answer

To find the probability of 3 people from town A and 2 people from town B in the council of 5 people, we need to calculate the total number of ways to choose 3 people from town A and 2 people from town B, and then divide it by the total number of ways to choose 5 people from the total of 20 people.

Let's denote:
- $$ A $$ as the number of people from town A,
- $$ B $$ as the number of people from town B,
- $$ C $$ as the number of people from town C,
- $$ T $$ as the total number of people.

Given:
- $$ A = 8 $$,
- $$ B = 7 $$,
- $$ C = 5 $$,
- $$ T = A + B + C = 8 + 7 + 5 = 20 $$.

We need to find the probability of 3 people from town A and 2 people from town B in the council of 5 people.

The total number of ways to choose 3 people from town A is $$ \binom{8}{3} $$ and the total number of ways to choose 2 people from town B is $$ \binom{7}{2} $$.

The total number of ways to choose 5 people from the total of 20 people is $$ \binom{20}{5} $$.

Therefore, the probability of 3 people from town A and 2 people from town B in the council of 5 people is:
$$ P = \frac{\binom{8}{3} \times \binom{7}{2}}{\binom{20}{5}} $$

Now, let's calculate the values of the binomial coefficients and then find the probability.
Calculate the value by following steps:
- step0: Calculate:
  $$ { }_{8}C_{3}$$
- step1: Expand the expression:
  $$\frac{8!}{3!\times \left(8-3\right)!}$$
- step2: Subtract the numbers:
  $$\frac{8!}{3!\times 5!}$$
- step3: Expand the expression:
  $$\frac{8\times 7\times 6\times 5\times 4\times 3!}{3!\times 5!}$$
- step4: Reduce the fraction:
  $$\frac{8\times 7\times 6\times 5\times 4}{5!}$$
- step5: Multiply the terms:
  $$\frac{6720}{5!}$$
- step6: Calculate the value:
  $$\frac{6720}{120}$$
- step7: Reduce the fraction:
  $$56$$
Calculate or simplify the expression $$ \binom{7}{2} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$ { }_{7}C_{2}$$
- step1: Expand the expression:
  $$\frac{7!}{2!\times \left(7-2\right)!}$$
- step2: Subtract the numbers:
  $$\frac{7!}{2!\times 5!}$$
- step3: Expand the expression:
  $$\frac{7\times 6\times 5\times 4\times 3\times 2!}{2!\times 5!}$$
- step4: Reduce the fraction:
  $$\frac{7\times 6\times 5\times 4\times 3}{5!}$$
- step5: Multiply the terms:
  $$\frac{2520}{5!}$$
- step6: Calculate the value:
  $$\frac{2520}{120}$$
- step7: Reduce the fraction:
  $$21$$
Calculate or simplify the expression $$ \binom{20}{5} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$ { }_{20}C_{5}$$
- step1: Expand the expression:
  $$\frac{20!}{5!\times \left(20-5\right)!}$$
- step2: Subtract the numbers:
  $$\frac{20!}{5!\times 15!}$$
- step3: Expand the expression:
  $$\frac{20\times 19\times 18\times 17\times 16\times 15!}{5!\times 15!}$$
- step4: Reduce the fraction:
  $$\frac{20\times 19\times 18\times 17\times 16}{5!}$$
- step5: Multiply the terms:
  $$\frac{1860480}{5!}$$
- step6: Calculate the value:
  $$\frac{1860480}{120}$$
- step7: Reduce the fraction:
  $$15504$$
Calculate or simplify the expression $$ 56*21/15504 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{56\times 21}{15504}$$
- step1: Multiply the numbers:
  $$\frac{1176}{15504}$$
- step2: Reduce the fraction:
  $$\frac{49}{646}$$
The probability of 3 people from town A and 2 people from town B in the council of 5 people is $$ \frac{49}{646} $$.
The probability of selecting 3 people from town A and 2 people from town B in the council of 5 is $$ \frac{49}{646} $$.

At the first tri-city meeting, there were 8 people from town people from town B, and 5 people from town . If the
council consists of 5 people, find the probability of 3 from town A and 2 from town B.

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At the first tri-city meeting, there were 8 people from town people from town B, and 5 people from town . If the council consists of 5 people, find the probability of 3 from town A and 2 from town B.

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At the first tri-city meeting, there were 8 people from town people from town B, and 5 people from town . If the
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