Nikki Has Five Shades 3 Of Them Match With 4 Of Her Hats And The Other 2 Matches With Her With 3 Of Her Other Hats. She Also Has 3 Wrist Watches And 1

Nikki has five shades 3 of them match with 4 of her hats and the other 2 matches with her with 3 of her other hats. She also has 3 wrist watches and 1 necklace that matches all combinations of shades and hats. how many 4-piece accessory combinations can he make?

A.54
B.56
C.60
D.648

 

\text{Combinations of shades and hats taken 1 each from 3 shades and 4 hats}\\= ^3C_1 \times ^4C_1=12\\\\\text{Combinations of shades and hats taken 1 each from 2 shades and 3 hats} \\= ^2C_1 \times ^3C_1=6\\\\\text{Total combinations of selecting shades and hats}=12+6=18.

No. of 4 piece accessory combinations

= (no. of combinations of shades and hats)×(no. of ways of selecting watch)×(no. of ways of selecting necklace)

= 18\times ^3C_1\times^1C_1\\=18\times3\times1=54


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