Question

political discussion group consists of 10 Democrats and 9 Republicans. Three members are selected to attend a conference. Find the probability that the group will consist of all Republicans.

Answer 1

solution

Democrats: 10

Republicans: 9

Total: 19

Let total to choose from be n:

Let number to be chosen be x:

The number of possible combinations can be obtained as:

$${n \choose x}$$

If 3 people are chosen from the group, the total number of possible combinations:

Let this be XT

$$XT = {19 \choose 3} = 969$$

If the 3 members are all chosen from Republicans, possible combinations:

Let this be XR

$$XR = {9 \choose 3} = 84$$

Probability that 3 chosen are all Republicans:

$$\frac{XR}{XT}$$

$$\frac{84}{969} = 0.0867$$

Answer: 0.0867