If words are formed using all the letters from the word ‘PERSONAL’ then identify the correct statement(s).

Question

If words are formed using all the letters from the word ‘PERSONAL’ then identify the correct statement(s). (A) Number of words which contain ‘SONA’ but not ‘SONAL’ is 5. (B) Number of words in which ‘EON’ does not occupy last three positions is 60.5! (C) Number of words in which vowels are in alphabetical order is 56.5! (D) Number of words which contain ‘PERSON’ but not ‘PERSONAL’, is 5

Tardigrade Admin · Accepted Answer

PERSONAL
(A) Required number of words = P, E, R, (SONA), L-P,E,R, (SONAL)

5! - 4! = 96

(B) Required number of words

= 8! - 5!

(C) Required number of words

=^{8} C_{5} \times 5! \times 1 = 56.5

!
(D) Required number of words

=

PERSON, A, L- PERSONAL

3! - 1 = 5

Q. If words are formed using all the letters from the word ‘PERSONAL’ then identify the correct statement(s).

Number of words which contain ‘SONA’ but not ‘SONAL’ is 5.

Number of words in which ‘EON’ does not occupy last three positions is 60.5!

Number of words in which vowels are in alphabetical order is 56.5!

Number of words which contain ‘PERSON’ but not ‘PERSONAL’, is 5

PERSONAL (A) Required number of words = P, E, R, (SONA), L-P,E,R, (SONAL) 5!−4!=96 (B) Required number of words =8!−5! (C) Required number of words =8C5​×5!×1=56.5 ! (D) Required number of words = PERSON, A, L- PERSONAL 3!−1=5

PERSONAL
(A) Required number of words = P, E, R, (SONA), L-P,E,R, (SONAL)
$5! - 4! = 96$
(B) Required number of words $= 8! - 5!$
(C) Required number of words $=^{8} C_{5} \times 5! \times 1 = 56.5$ !
(D) Required number of words $=$ PERSON, A, L- PERSONAL
$3! - 1 = 5$