Question

Three students from grades 10, 11, and 12 were elected to the Student Council.Grade 10: Tom (T), Sally (S), and Bill (B)Grade 11: Jerry (J), Anne (A), and Connie (C)Grade 12: Dan (D), Martha (M), and Gwen (G)A three-member committee is to be formed with one person from each grade. All possible combinations must be considered before a decision is made. Two possible combinations are Tom, Jerry, and Dan (TJD) and Sally, Anne, and Martha (SAM). List all other possible combinations for the committee.

Answer 1

Tom, Jerry, Martha (TJM)

Tom, Jerry, Gwen (TJG)

Tom, Anne, Dan, (TAD)

Tom, Anne, Martha, (TAM)

Tom, Anne, Gwen (TAG)

Tom, Connie, Dan (TCD)

Tom, Connie, Martha (TCM)

Tom, Connie, Gwen (TCG)

Sally, Jerry, Dan (SJD)

Sally, Jerry, Martha (SJM)

Sally, Jerry, Gwen (SJG)

Sally, Anne, Dan (SAD)

Sally, Anne, Gwen (SAG)

Sally, Connie, Dan (SCD)

Sally, Connie, Martha (SCM)

Sally, Connie, Gwen (SCG)

Bill, Jerry, Dan (BJD)

Bill, Jerry, Martha (BJM)

Bill, Jerry, Gwen (BJG)

Bill, Anne, Dan (BAD)

Bill, Anne, Martha (BAM)

Bill, Anne, Gwen (BAG)

Bill, Connie, Dan (BCD)

Bill, Connie, Martha (BCM)

Bill, Connie, Gwen (BCG)

Explanation:

Data:

Grade 10: Tom (T), Sally (S), Bill (B)

Grade 11: Jerry (J), Anne (A), Connie (C)

Grade 12: Dan (D), Martha (M), Gwen (G)

We need to form a three-member committee with one person from each grade using all possible combinations. We are already given 2 possible combinations: Tom, Jerry, Dan (TJD) and Sally, Anne, Martha (SAM).

We just need to form the other combinations, one member for each grade (repeated combinations are not allowed):

Combinations:

Tom, Jerry, Martha (TJM)

Tom, Jerry, Gwen (TJG)

Tom, Anne, Dan, (TAD)

Tom, Anne, Martha, (TAM)

Tom, Anne, Gwen (TAG)

Tom, Connie, Dan (TCD)

Tom, Connie, Martha (TCM)

Tom, Connie, Gwen (TCG)

Sally, Jerry, Dan (SJD)

Sally, Jerry, Martha (SJM)

Sally, Jerry, Gwen (SJG)

Sally, Anne, Dan (SAD)

Sally, Anne, Gwen (SAG)

Sally, Connie, Dan (SCD)

Sally, Connie, Martha (SCM)

Sally, Connie, Gwen (SCG)

Bill, Jerry, Dan (BJD)

Bill, Jerry, Martha (BJM)

Bill, Jerry, Gwen (BJG)

Bill, Anne, Dan (BAD)

Bill, Anne, Martha (BAM)

Bill, Anne, Gwen (BAG)

Bill, Connie, Dan (BCD)

Bill, Connie, Martha (BCM)

Bill, Connie, Gwen (BCG)