Question

How many 6-letter words with distinct letters in each can be formed using the letters of the word EDUCATION? How many of these begin with I

• A. ${}^9{P}_{6^{\prime }}$ ${}^8{P}_5$
• B. ${}^9{P}_{6^{\prime }}$ ${}^9{P}_5$
• C. ${}^8{P}_{6^{\prime }}$ ${}^8{P}_5$
• D. ${}^8{P}_{6^{\prime }}$ ${}^8{P}_4$

Answer 1

Answer: (A)

${}^9{P}_{6^{\prime }}$ ${}^8{P}_5$

The word EDUCATION is formed using the $9$ distinct letters E,D,U,C,A,T,I,O,N
So, number of $6$ letter words with distinct letters that be formed using these $9$ letters is ${9_P}_6$
And when the first letter is I, then the remaining $5$ letters can be formed using the remaining $8$ letters in ${8_P}_5$ ways.