Question 56

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?

Solution

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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