M May

Santa’s Gnomes all insist on wearing different outfits.

Santa orders hats, coats, trousers and boots

How many different gnomes can Santa have?

Hats can be red, orange, yellow, green, blue, indigo and violet

Coats can be red, orange, yellow, green, blue, indigo and violet

Trousers can be red, blackblack, green, blue and gold

Boots can be red and blackblack

M May

Santa’s Gnomes have different outfits.

red

orange

yellow

green

blue

indigo

violet

red

orange

yellow

green

blue

indigo

violet

red

blackblack

red

blackblack

green

blue

gold

Hats Coats Trousers Boots

M May

Hats, Coats,….

red, red orange, red yellow, red green, red blue red indigo red violet red

red, orange orange, orange yellow, orange green, orange blue orange indigo orange violet orange

red, yellow orange , yellow yellow, yellow green, yellow blue yellow indigo yellow violet yellow

red, green orange, green yellow green green green blue green indigo green violet green

red, blue orange, blue yellow, blue green, blue blue blue indigo blue violet blue

red, indigo orange, indigo yellow, indigo green, indigo blue indigo indigo indigo violet indigo

red, violet orange violet yellow violet green violet blue violet indigo violet violet violet

M May

Hats, Coats, Trousers, …..

all 49 with red trousers

and then all 49 with black trousersblack trousers

red, red orange, red yellow, red green, red blue red indigo red violet red

red, orange orange, orange yellow, orange green, orange blue orange indigo orange violet orange

red, yellow orange , yellow yellow, yellow green, yellow blue yellow indigo yellow violet yellow

red, green orange, green yellow green green green blue green indigo green violet green

red, blue orange, blue yellow, blue green, blue blue blue indigo blue violet blue

red, indigo orange, indigo yellow, indigo green, indigo blue indigo indigo indigo violet indigo

red, violet orange violet yellow violet green violet blue violet indigo violet violet violet

M May

Hats, Coats, Trousers, …..

also all 49 with green trousers

and then all 49 with blue trousers, and also 49 with gold trousers

red, red orange, red yellow, red green, red blue red indigo red violet red

red, orange orange, orange yellow, orange green, orange blue orange indigo orange violet orange

red, yellow orange , yellow yellow, yellow green, yellow blue yellow indigo yellow violet yellow

red, green orange, green yellow green green green blue green indigo green violet green

red, blue orange, blue yellow, blue green, blue blue blue indigo blue violet blue

red, indigo orange, indigo yellow, indigo green, indigo blue indigo indigo indigo violet indigo

red, violet orange violet yellow violet green violet blue violet indigo violet violet violet

M May

red

blackblack

green

blue

gold

All 49 hats and coats combinations with Trousers

49 x 5 = 245

All 245 hats and coats and trousers combinations with Bootsred

blackblack

245 x 2 = 490 different outfits are possible

So it is possible for Santa to have 490 gnomes.

M May

Hats, Coats, Trousers, Boots

red

orange

yellow

green

blue

indigo

violet

red

orange

yellow

green

blue

indigo

violet

red

blackblack

red

blackblack

green

blue

gold

7 7

5

2

So Total number of outfits for Santa’s gnomes is

7 x 7 x 5 x 3 = 490

So, the choices lead to : ……

Santa can have 490 gnomes!