JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is

    A) \[{{105}^{5}}\]         

    B) \[210\times 243\]

    C) \[105\times 243\]          

    D) \[150\times {{21}^{2}}\]

    Correct Answer: D

    Solution :

    [d] Let us first select two places for vowel, which can be selected from 4 places in \[^{4}{{C}_{2}}\]ways. Now this places can be filled by vowels in \[5\times 5=25\]ways as repletion is allowed. The remaining two places can be filled by consonants in \[21\times 21\]ways. Then the total number of words is \[^{4}{{C}_{2}}\times 25\times {{21}^{2}}=150\times {{21}^{2}}\].

You need to login to perform this action.
You will be redirected in 3 sec spinner