Asenate committee consists of 5 republicans, 6 democrats, and 2 independents. a subcommittee of 3 members is randomly chosen. what is the probability that the subcommittee consists of 1 republican, 1 democrat, and 1 independent?

Solution:

The total number of ways to form a 3 person subcommittee is 13C3 = 286  

The total number of ways to choose 1 republican from 5 is 5C1 = 5.

The total number of ways to choose 1 democrat from 6 is 6C1 = 6.

The total number of ways to choose 1 independent from 2 is 2C1 = 2.

By the counting principle, there are 5 x 6 x 2 = 60 ways to select 1 republican, 1 democrat and 1 independent  

Therefore the probability that the subcommittee consists of 1 Republican, 1 Democrat, and 1 Independent is:

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9

step-by-step explanation: