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 combinatons are Tom, Jerry, and Dan (TJD) and Sally, Anne, and Martha (SAM). List all other possible combinations for the committee.

tjd, tjm, tjg, tad, tam, tag, tcd, tcm, tcg, sjd, sjm, sjg, sad, sam, sag, scd, scm, scg, bjd, bjm, bjg, bad, bam, bag, bcd, bcm ,bcg

1)BCG

2)TJM
3)TJG
4)TAD
5)TAM
6)TAG
7)TCD
8)TCM
9)TCG
10)SJD
11)SJM
12)SJG
13)SAD
14)SAG
15)SCD
16)SCM
17)SCG
18)BJD
19)BJM
20)BJG
21)BAD
22)BAM
23)BAG
24)BCD
25)BCM

Thank you! This was correct.

To find all other possible combinations for the committee, we need to consider taking one person from each grade (10th, 11th, and 12th). We have already mentioned two possible combinations: Tom, Jerry, and Dan (TJD) and Sally, Anne, and Martha (SAM).

To generate all other combinations, we can try various permutations of the remaining students from each grade. Here is the step-by-step process to find all the possible combinations:

1. Start with the first person from the remaining students in Grade 10. In this case, it is Bill (B).

2. Move to the next grade, Grade 11, and select a person. Since Jerry (J) is already included in TJD, we will choose Anne (A).

3. Move to the last grade, Grade 12, and select a person. We have Dan (D) in TJD, so Gwen (G) will be the final member of this combination. Thus, the combination is BAG.

4. Now, we move back to Grade 11 and consider the remaining student, Jerry (J). We select Sally (S) from Grade 10, and then from Grade 12, we select Martha (M). The combination becomes JSM.

5. Moving forward in Grade 11, we pick Connie (C) and Tom (T) from Grade 10 and Grade 12, respectively. The combination will be CTT.

Therefore, the possible combinations for the three-member committee are:
1. TJD (Tom, Jerry, Dan)
2. SAM (Sally, Anne, Martha)
3. BAG (Bill, Anne, Gwen)
4. JSM (Jerry, Sally, Martha)
5. CTT (Connie, Tom, Tom)

Please note that each person can only be selected once, and we have considered all possible combinations by selecting one person from each grade.

there are 27 such combinations.

Do you actually expect somebody to list those for you?
go about it systematically:
TJD
TJM
TJG
etc