Aptitude Discussion

Q. |
There are 6 positive and 8 negative numbers. Four numbers are chosen at random and multiplied. The probability that the product is a positive number is: |

✖ A. |
500/1001 |

✖ B. |
503/1001 |

✔ C. |
505/1001 |

✖ D. |
101/1001 |

**Solution:**

Option(**C**) is correct

The product of four numbers will be positive in the following ways.

All the four numbers are positive, hence probability:

\(=\dfrac{^6C_4}{^{14}C_4}\)

All the four numbers are negative, hence probability:

\(=\dfrac{^8C_4}{^{14}C_4}\)

Two numbers are positive and two are negative, hence Probability:

\(=\dfrac{^6C_2\times ^8C_2}{^{14}C_4}\)

Hence, required probability of the event:

\(=\dfrac{^6C_4+^8C_4+(^6C_2\times ^8C_2)}{^{14}C_4}\)

\(=\dfrac{15+70+15\times 28}{1001}\)

\(=\dfrac{505}{1001}\)

**Poonam Pipaliya**

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I am not able to understand your point, it would be nice if you elaborate more.

sir it is not in options but we can also add the way 6C1*8C3 or 6C3*8C1 iwith 505,,,,aren't we...??..!!