Q53 / 90 · JEE Main 2012 (19 May Online) · Mathematics

The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is

  • Correct answer
    A
    96
  • B
    128
  • C
    24
  • D
    72

Solution

There are 2 vowels and 4 consonants in the letters $a, b, c, d, e, f$. If we select one vowel, then number of arrangements $$ ={ }^2 C_1 \times{ }^4 C_2 \times 3 !=2 \times \frac{4 \times 3}{2} \times 3 \times 2=72 $$ If we select two vowels, then number of arrangements $$ ={ }^2 C_2 \times{ }^4 C_1 \times 3 !=1 \times 4 \times 6=24 $$ Hence, total number of arrangements $$ =72+24=96 $$

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

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