Aptitude Discussion

Q. |
A box contains $10$ balls out of which $3$ are red and rest are blue. In how many ways can a random sample of $6$ balls be drawn from the bag so that at the most $2$ red balls are included in the sample and no sample has all the $6$ balls of the same colour? |

✖ A. |
$105$ |

✔ B. |
$168$ |

✖ C. |
$189$ |

✖ D. |
$120$ |

**Solution:**

Option(**B**) is correct

Six balls can be selected in the following ways:

One red ball and 5 blue ball

Or

Two red balls and 4 blue balls

Total number of ways:

$= ({^3C_1} × {^7C_5}) + ({^3C_2} × {^7C_4})$

$= 63 + 105$

$= \textbf{168}$