Permutations

The number of ways in which 3 things can be chosen from among 7 things and arranged in a row is the product of the 3 consecutive numbers

7·6·5

starting at 7.

So there are 210 ways to choose 3 things from 7 and arrange them in a row.

If the seven things are the letters ROYGBIV, standing for Red, Orange, Yellow, Green, Blue, Indigo, and Violet, then the 210 ways are

ROY ROG ROB ROI ROV   ORY ORG ORB ORI ORV   YRO YRG YRB YRI YRV
RYO RYG RYB RYI RYV   OYR OYG OYB OYI OYV   YOR YOG YOB YOI YOV
RGO RGY RGB RGI RGV   OGR OGY OGB OGI OGV   YGR YGO YGB YGI YGV
RBO RBY RBG RBI RBV   OBR OBY OBG OBI OBV   YBR YBO YBG YBI YBV
RIO RIY RIG RIB RIV   OIR OIY OIG OIB OIV   YIR YIO YIG YIB YIV
RVO RVY RVG RVB RVI   OVR OVY OVG OVB OVI   YVR YVO YVG YVB YVI

GRO GRY GRB GRI GRV   BRO BRY BRG BRI BRV   IRO IRY IRG IRB IRV
GOR GOY GOB GOI GOV   BOR BOY BOG BOI BOV   IOR IOY IOG IOB IOV
GYR GYO GYB GYI GYV   BYR BYO BYG BYI BYV   IYR IYO IYG IYB IYV
GBR GBO GBY GBI GBV   BGR BGO BGY BGI BGV   IGR IGO IGY IGB IGV
GIR GIO GIY GIB GIV   BIR BIO BIY BIG BIV   IBR IBO IBY IBG IBV
GVR GVO GVY GVB GVI   BVR BVO BVY BVG BVI   IVR IVO IVY IVG IVB

VRO VRY VRG VRB VRI
VOR VOY VOG VOB VOI
VYR VYO VYG VYB VYI
VGR VGO VGY VGB VGI
VBR VBO VBY VBG VBI
VIR VIO VIY VIG VIB

Can you see the 7, the 6, and the 5 in this pattern?
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