Q55 / 160 · TS EAMCET 2019 (04 May Shift 1) · Mathematics

The number of 4 letter permutations formed with English alphabet such that the number of distinct vowels is equal to the number of distinct consonants, when repetition is allowed, is

  • A
    630
  • B
    $3^5 \times 70$
  • Correct answer
    C
    $3^6 \times 70$
  • D
    $3^4 \times 60$

Solution

The permutation of 4 letters such that voweI and consonants are equal $$ \begin{aligned} { }^{21} C_1 & \times{ }^5 C_1 \times \frac{4 !}{2 ! 2 !}+{ }^{21} C_2 \times{ }^5 C_2 \times 4 ! \\ & =21 \times 5 \times 6+21 \times 10 \times 5 \times 2 \times 24 \\ & =630+50400 \\ & =51030 \\ & =729 \times 70=3^6 \times 70 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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