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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

  • question_answer
    If letters of the word 'CALCULUS' are arranged such a way that all C's occur before all L's, then the total number of words formed is

    A)  600                            

    B)  820

    C)  840                            

    D)  620

    Correct Answer: C

    Solution :

     CALCULUS \[\square \]       \[\square \]       \[\square \]       \[\square \]       \[\square \]       \[\square \]       \[\square \]       \[\square \] All C?s occur before all L?s is \[^{8}{{C}_{4}}=\frac{8!}{4!4!}=\frac{8\times 7\times 6\times 5}{24}=70\] Now, there are four places remaining. These places are filled by the letters (A, U, U, S). So, number of ways of filling those four places \[=\frac{4!}{2!}=12\] Total words \[=70\times 12=840\]


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