Question

steven has 9 different shirts 5 different hats 4 different scarves. Steven thinks that if he picks just two of the three items of clothing there will be more than 180 combinations. is the correct

Answer 1

no

Explanation:

no, because;

if steven was to wear one of the 9 shirts and one of the 5 different hats, the total would be 45, which is below 180

also if steven was to wear one of 9 shirts and one of the 4 different scarves, the total would be 36

and if steven was to wear one of the 4 different scarves and one of the 5 different hats the total would be 20. 45+36+20=101

101 does not exceed 180

Answer 2

Steven is incorrect.

Explanation:

Steven has

• 9 different shirts
• 5 different hats
• 4 different scarves.

He picks just two of the three items of clothing. This can be made in

• 
  `9\cdot 5=45` different ways to choose shirt and hat;
• 
  `5\cdot 4=20` different ways to choose hat and scarf;
• 
  `9\cdot 4=36` different ways to choose shirt and scarf.

In total, there are

`45+20+36=101`

different ways to pick just two of the three items of clothing.

Since
`101<180,` Steven is incorrect.