A membership committee of three is formed from four eligible members. Let the eligible members be represented by A, B, C, and D. The possible outcomes include S = {ABC, ABD, ACD, BCD}.
Which statements about the situation are true? Check all that apply.

There are four ways to choose the committee.
There are three ways to form the committee if person D must be on it.
If seven members are eligible next year, then there will be fewer combinations.
If persons B and C must be on the committee, there are two ways to form the committee.
If persons A and C must be on the committee, then there is only one way to form the committee.

From the given sample space of S = {ABC, ABD, ACD, BCD}, it can be concluded that;

(1) There are four ways to choose the committee.
(2) There are three ways in which person D is included.
(3) If persons B and C must be included, there are two ways to form the committee.

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MrRoyal MrRoyal · Answer 2 · 2022-01-21T17:34:33+01:00

The true statements are:

(a) There are four ways to choose the committee.

(b) There are three ways to form the committee if person D must be on it.

(d) If persons B and C must be on the committee, there are two ways to form the committee.

The possible outcomes (i.e. the sample space) are given as:

S = {ABC, ABD, ACD, BCD}

From the above highlight, we have the following points

The sample size is 4
There are two outcomes that include B and C
There are three outcomes that include D

The above highlights mean that:

Options (a), (b) and (d) are correct