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

asked Jan 4, 2020 196k views

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Bob Whiteman · Answer 1 · 2020-01-11T15:58:14+0000

Answer:

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: