dayshawn can choose two of his four t - shirts to take on a weekend trip. if the t - shirts are labeled a…

dayshawn can choose two of his four t - shirts to take on a weekend trip. if the t - shirts are labeled a, b, c, and d, which choice represents the sample space, s, for the event?\ns = {abcd}\ns = {abcd, dcba}\ns = {ab, ac, ad, bc, bd, cd}\ns = {ab, ba, ac, ca, ad, da, bc, cb, bd, db, cd, dc}

dayshawn can choose two of his four t - shirts to take on a weekend trip. if the t - shirts are labeled a, b, c, and d, which choice represents the sample space, s, for the event?\ns = {abcd}\ns = {abcd, dcba}\ns = {ab, ac, ad, bc, bd, cd}\ns = {ab, ba, ac, ca, ad, da, bc, cb, bd, db, cd, dc}

Answer

Explanation:

Step1: Understand sample - space concept

The sample space is the set of all possible outcomes. Here, we are choosing 2 - shirt combinations out of 4 shirts (A, B, C, D) and the order of selection does not matter (since taking shirt A and shirt B is the same as taking shirt B and shirt A for the purpose of packing for the trip).

Step2: List all combinations

We list all pairs: AB, AC, AD, BC, BD, CD.

Answer:

S = {AB, AC, AD, BC, BD, CD}