Permutation-Combination
Aptitude

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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.

$1,701$

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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,

$= 3 × 7 × 27 × 3$

$= \textbf{1701 ways.}$


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