Seven-letter words can be formed without repetition from the letters of the word INCLUDE; 5040. How many have the letters N and D separated by exactly two letters?
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
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