The number of 4 letter words that can be form | vedclass

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Question

(C) The word $EQUATION$ consists of $8$ distinct letters: $E, Q, U, A, T, I, O, N$. Total number of $4$ letter words that can be formed using these $8

Vedclass · Accepted Answer

$2416$

Vedclass · Answer

(C) The word $EQUATION$ consists of $8$ distinct letters: $E, Q, U, A, T, I, O, N$. Total number of $4$ letter words that can be formed using these $8$ letters (with repetition allowed) is $8^4 = 4096$. Number of $4$ letter words that can be formed with distinct letters (no repetition) is given by the permutation formula $^8P_4 = 8 	imes 7 	imes 6 	imes 5 = 1680$. The number of $4$ letter words with at least one letter repeated is the total number of words minus the number of words with no letters repeated: $= 8^4 - ^8P_4 = 4096 - 1680 = 2416$.

The number of $4$ letter words that can be formed with the letters in the word $EQUATION$ with at least one letter repeated is

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