Aptitude Discussion

Q. |
While packing for a business trip Mr. Debashis has packed 3 pairs of shoes, 4 pants, 3 half-pants,6 shirts, 3 sweater and 2 jackets. The outfit is defined as consisting of a pair of shoes, a choice of "lower wear" (either a pant or a half-pant), a choice of "upper wear" (it could be a shirt or a sweater or both) and finally he may or may not choose to wear a jacket. How many different outfits are possible? |

✖ A. |
$567$ |

✖ B. |
$1,821$ |

✖ C. |
$743$ |

✔ D. |
$1,701$ |

**Solution:**

Option(**D**) is correct

Number of ways a pair of shoes can be selected $= {^3C_1} = 3$ ways.

Number of ways "lower wear" can be selected $= (3 + 4) = 7$ ways

Number of ways "upper wear" can be selected $= 3 + 6 + 3 × 6 = 27$ ways

Number of ways jacket can be chosen or not chosen $= 3$ ways {No jacket, 1st jacket, 2nd jacket)

⇒ Total number of different outfits,

$= 3 × 7 × 27 × 3$

$= \textbf{1701 ways.}$