# Moderate Permutation-Combination Solved QuestionAptitude 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,

$= 3 × 7 × 27 × 3$

$= \textbf{1701 ways.}$