Question

permutations
sheet 1
list out all the possible permutations.

1. a, e, i, o, u - taken two at a time
2. 4, 2, 3
3. cat(c), dog(d), rabbit(r), fish(f) - taken three at a time
4. blue(b), orange(o), yellow(y), red(r), white(w), green(g) - taken two at a time
5. △ ▭

Explanation:

Step1: Solve for 2-at-a-time vowels

First, fix each vowel as the first element, then pair with remaining vowels:
A: AE, AI, AO, AU
E: EA, EI, EO, EU
I: IA, IE, IO, IU
O: OA, OE, OI, OU
U: UA, UE, UI, UO

Step2: Solve for full permutations of 4,2,3

List all ordered arrangements of the 3 numbers:
423, 432, 243, 234, 342, 324

Step3: Solve for 3-at-a-time animal codes

Fix each code as the first element, then pair with all unique 2-code permutations of the remaining:
C: CDR, CDF, CRD, CRF, CFD, CFR
D: DCR, DCF, DRC, DRF, DFC, DFR
R: RCD, RCF, RDC, RDF, RFC, RFD
F: FCD, FCR, FDC, FDR, FRC, FRD

Step4: Solve for 2-at-a-time color codes

Fix each code as the first element, then pair with remaining codes:
B: BO, BY, BR, BW, BG
O: OB, OY, OR, OW, OG
Y: YB, YO, YR, YW, YG
R: RB, RO, RY, RW, RG
W: WB, WO, WY, WR, WG
G: GB, GO, GY, GR, GW

Step5: Solve for shape permutations

List all ordered arrangements of the 2 shapes:
△□, □△

Answer:

1. AE, AI, AO, AU, EA, EI, EO, EU, IA, IE, IO, IU, OA, OE, OI, OU, UA, UE, UI, UO
2. 423, 432, 243, 234, 342, 324
3. CDR, CDF, CRD, CRF, CFD, CFR, DCR, DCF, DRC, DRF, DFC, DFR, RCD, RCF, RDC, RDF, RFC, RFD, FCD, FCR, FDC, FDR, FRC, FRD
4. BO, BY, BR, BW, BG, OB, OY, OR, OW, OG, YB, YO, YR, YW, YG, RB, RO, RY, RW, RG, WB, WO, WY, WR, WG, GB, GO, GY, GR, GW
5. △□, □△