The composition of the Senate of the 107th Congress is 50 Re

The composition of the Senate of the 107^th Congress is 50 Republicans, 49 Democrats, and 1 Independent. A new committee is being formed to study ways to benefit the arts in education. If 3 senators are selected at random to head the committee, find the probability of the following.

Enter you answers as fractions or as decimals rounded to 3 decimal places.

The group of 3 consists of 1 from each party, including the Independent.

P (1 Democrat, 1 Republican, 1 Independent)= ?

Solution

There are 100C3 = 161700 ways to choose any 3 members.

Meanwhile, there are (50 rep)(49 dem)(1 ind) = 2450 ways to choose 1 member from each denomination.

Thus,

P(1D, 1R, 1I) = 2450/161700 = 0.015151515 = 0.015 [ANSWER]