P[knew answer|correct answer]=P[correct answer | knew answer]P[knew answer]P[correct answer]
P[knew answer]=12P[correct answer|knew answer]=1P[correct answer]=12+12(1413+3414)=6196
P[knew answer|correct answer]=1⋅126196=4861
Pick a card any card. Probability of this is 1.
Now pick a card not duplicate to the first card. Probability of this is 46/47
Continuing we have
p=14647444642454044=112141
Select the slot that N and D will occupyThere are 4 of theseSelect the ordering of N and D within the slotThere are two arrangementsThere are now 5 unique remaining lettersThese can be arranged 5! ways in the remaining slotsSo there are 4⋅2⋅5!=960 valid arrangementsThere are a total of 7!=5040 possible arrangementsp=9605040=421
p=(42)(111)+(52)(101)+(62)(91)(153)
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