The starting lineup for a basketball team is to consist of two forwards and three guards. Two brothers are on the team. Matthew is a forward and Tony a guard there are four forwards and six guards from which to choose the lineup if the starting players are chosen at random. What is the probability that the two brothers will end up in the starting lineup?

Question

The starting lineup for a basketball team is to consist of two forwards and three guards. Two brothers are on the team. Matthew is a forward and Tony a guard there are four forwards and six guards from which to choose the lineup if the starting players are chosen at random. What is the probability that the two brothers will end up in the starting lineup?

Answer 1

There are a total of 6 possible players that can be chosen for the forward position, and 4 possible players that can be chosen for the guard position.

The probability that Matthew is chosen as one of the forwards is 1 out of 6, or 1/6.
The probability that Tony is chosen as one of the guards is 1 out of 4, or 1/4.

Therefore, the probability that both Matthew and Tony are chosen for their respective positions is (1/6) * (1/4) = 1/24.

So, the probability that the two brothers will end up in the starting lineup is 1/24.

Answer 2

To find the probability that the two brothers will end up in the starting lineup, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

First, let's determine the number of favorable outcomes where the two brothers are in the starting lineup.

We have two brothers, Matthew and Tony. Matthew is already selected as one of the forwards. We need to select one more forward and three guards.

Since there are four forwards to choose from (including Matthew) and three guards to select from the six non-brother guards, the number of favorable outcomes is:

Number of favorable outcomes = 1 (for Matthew) * 4 (for the other forward) * 6C3 (for the three guards)
= 1 * 4 * 20
= 80

Next, let's determine the total number of possible outcomes without any restrictions.

We need to select two forwards from a total of four forwards and three guards from a total of six guards.

The number of total possible outcomes is given by:

Number of total possible outcomes = 4C2 (for the two forwards) * 6C3 (for the three guards)
= 6 * 20
= 120

Now, we can calculate the probability.

Probability = Number of favorable outcomes / Number of total possible outcomes
= 80 / 120
= 2/3

Therefore, the probability that the two brothers will end up in the starting lineup is 2/3.