Question

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

• A. $2400$
• B. $2408$
• C. $2416$
• D. $2432$

Answer 1

Answer: (C)

$2416$

Number of distinct alphabets in the word EQUATION is 8

Number of 4 letter words that can be formed with repetition $=8\times 8\times 8\times 8=4096$

Number of 4 letter words that can be formed without repetition $=8\times 7\times 6\times 5=1680$

Number of 4 letter words that can be formed with atleast one repetition $=$ (Number of 4 letter words that can be formed with repetition)-(Number of 4 letter words that can be formed without repetition)

$=4096-1680=2416$

Hence the answer is option (C)