1. 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?
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By: anil on 05 May 2019 02.40 am
Let us find out the number of ways in which an outfit can be selected.
An outfit is defined as a pair of shoes, an upper wear, and a lower wear.
A pair of shoes can be selected in 3 ways.
There are 4 pants and 3 half-pants.
A pant or a half-pant can be selected in 7 ways.
A shirt can be selected in 6 ways.
A sweater can be selected in 3 ways.
A shirt and a sweater can be selected in 18 ways.
Therefore, an upper wear can be selected in 6+3+18 = 27 ways.
A jacket can be worn in 1 (no jacket is selected) + 2 (one of the 2 jackets is selected) = 3 ways.
Therefore, the total number of ways in which an outfit can be worn = 3*7*27*3 = 1701.
As the answer is not among the given choices, option D is the right answer.
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An outfit is defined as a pair of shoes, an upper wear, and a lower wear.
A pair of shoes can be selected in 3 ways.
There are 4 pants and 3 half-pants.
A pant or a half-pant can be selected in 7 ways.
A shirt can be selected in 6 ways.
A sweater can be selected in 3 ways.
A shirt and a sweater can be selected in 18 ways.
Therefore, an upper wear can be selected in 6+3+18 = 27 ways.
A jacket can be worn in 1 (no jacket is selected) + 2 (one of the 2 jackets is selected) = 3 ways.
Therefore, the total number of ways in which an outfit can be worn = 3*7*27*3 = 1701.
As the answer is not among the given choices, option D is the right answer.