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

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Question

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

Vedclass · Accepted Answer

$12240$

Vedclass · Answer

(B) Total letters in the alphabet = $26$. 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 ways to form a $3$-letter password without repetition = $P(26, 3) = 26 	imes 25 	imes 24 = 15600$. Ways to form a $3$-letter password using only asymmetric letters = $P(16, 3) = 16 	imes 15 	imes 14 = 3360$. Ways with at least one symmetric letter = $	ext{Total ways} - 	ext{Ways with no symmetric letters} = 15600 - 3360 = 12240$.

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