Q256 / 270 · NDA 2015 (Phase 2) · Mathematics

Three digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that the product is odd ?

  • A
    2/3
  • B
    7/48
  • Correct answer
    C
    5/42
  • D
    5/108

Solution

Total no. of 3-digit numbers $=9 \times 8 \times 7=504$ For product to be odd, we have to choose only from odd numbers. $\therefore$ Total no. of 3-digit no. whose product are odd $=5 \times 4 \times 3=60$ $\therefore$ Required probability $=\frac{60}{504}=\frac{5}{42}$

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

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