Each of the 10 letters A, H, I, M, O, T, U, V | vedclass

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(B) There are $26$ letters in the alphabet.Number of symmetric letters = $10$.Number of asymmetric letters = $26 - 10 = 16$.We need to form a $3$-lett

Vedclass · Accepted Answer

$12240$

Vedclass · Answer

(B) There are $26$ letters in the alphabet.Number of symmetric letters = $10$.Number of asymmetric letters = $26 - 10 = 16$.We need to form a $3$-letter password with at least one symmetric letter.Total number of ways to form a $3$-letter password (without repetition) is $P(26, 3) = 26 	imes 25 	imes 24 = 15600$.Number of ways to form a $3$-letter password using only asymmetric letters is $P(16, 3) = 16 	imes 15 	imes 14 = 3360$.Number of ways with at least one symmetric letter = (Total ways) - (Ways with no symmetric letters).$= 15600 - 3360 = 12240$.

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