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?
Correct Answer: 1701
Number of ways a pair of shoes can be selected,= 3C1
= 3 waysNumber of ways lower wear can be selected = (3 + 4) = 7 ways.Number of ways upper wear can be selected,= 3 + 6 + (3 × 6)
= 27 waysNumber 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
= 1701 ways
= 3 waysNumber of ways lower wear can be selected = (3 + 4) = 7 ways.Number of ways upper wear can be selected,= 3 + 6 + (3 × 6)
= 27 waysNumber 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
= 1701 ways