Consider the 10 lettered word W = C U R R I C U L U M. Number of ways in which 5 lettered words can be formed using the letters from the word 'W' if each 5 lettered word has exactly 3 different letters, is

Question

Consider the 10 lettered word W = C U R R I C U L U M. Number of ways in which 5 lettered words can be formed using the letters from the word 'W' if each 5 lettered word has exactly 3 different letters, is (A) 360 (B) 560 (C) 610 (D) 720

Tardigrade Admin · Accepted Answer

U's arrow 3 ; C's arrow 2 ; R's arrow 2 ; L's arrow 1 ; I's arrow 1 ; M's arrow 1 Case-I: 3 Alike and 2 different Number of words formed =1 × 5 C 2 × (5 !/3 !)=10 × 20=200. Case-II: 2 Alike, 2 others alike and 1 different Number of words formed = 3 C 2 × 4 C 1 × (5 !/2 ! 2 !)=12 × 30=360.

Q. Consider the 10 lettered word W = C U R R I C U L U M. Number of ways in which 5 lettered words can be formed using the letters from the word 'W' if each 5 lettered word has exactly 3 different letters, is

360

560

610

720

U's →3; C's →2; R's →2; L's →1; I's →1; M's →1 Case-I : 3 Alike and 2 different Number of words formed =1×5C2​×3!5!​=10×20=200. Case-II: 2 Alike, 2 others alike and 1 different Number of words formed =3C2​×4C1​×2!2!5!​=12×30=360.

Q. Consider the 10 lettered word W = C U R R I C U L U M.
Number of ways in which 5 lettered words can be formed using the letters from the word 'W' if each 5 lettered word has exactly 3 different letters, is