Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is :

Question

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is : (A) ( beginarrayl8 4 endarray)- 8 P4 (B) 84+( beginarrayl8 4 endarray) (C) 84- 8 P4 (D) 84-( beginarrayl8 4 endarray)

Tardigrade Admin · Accepted Answer

Total number of words formed by 4 letters given from eight different letters with repetition =84 and number of words with no repetition = 8 P4 ∴ Required number of words =84- 8 P4

Q. Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is :

$(84) -^{8} P_{4}$

$8^{4} + (84)$

$8^{4} -^{8} P_{4}$

$8^{4} - (84)$

Total number of words formed by $4$ letters given from eight different letters with repetition $= 8^{4}$ and number of words with no repetition $=^{8} P_{4}$
$∴$ Required number of words $= 8^{4} -^{8} P_{4}$

Q. Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is :

(84​)−8P4​

84+(84​)

84−8P4​

84−(84​)

Total number of words formed by 4 letters given from eight different letters with repetition =84 and number of words with no repetition =8P4​ ∴ Required number of words =84−8P4​

$(84) -^{8} P_{4}$

$8^{4} + (84)$

$8^{4} -^{8} P_{4}$

$8^{4} - (84)$

Total number of words formed by $4$ letters given from eight different letters with repetition $= 8^{4}$ and number of words with no repetition $=^{8} P_{4}$
$∴$ Required number of words $= 8^{4} -^{8} P_{4}$