14 John has 8 different shirts 6 different hats. 4 different scarves. (a) On Monday, he picks a shirt, a hat and a scarf. Show that there are 192 different combinations he can pick. (b) John thinks that if he picks just two of the three items of clothing there will be more than 192 combinations. Is he correct? Show your reasoning.

GCSE OCR Maths Probability: 14 John has 8 different shirts

14 John has 8 different shirts 6 different hats - OCR - GCSE Maths - Question 14 - 2017 - Paper 1

Question 14

14 John has 8 different shirts 6 different hats. 4 different scarves. (a) On Monday, he picks a shirt, a hat and a scarf. Show that there are 192 different combin... show full transcript

Worked Solution & Example Answer:14 John has 8 different shirts 6 different hats - OCR - GCSE Maths - Question 14 - 2017 - Paper 1

Step 1

Show that there are 192 different combinations he can pick.

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Answer

To find the total number of combinations John can pick, we multiply the number of different options for each item of clothing.

The number of shirts is 8, the number of hats is 6, and the number of scarves is 4. Therefore, the total number of combinations is given by:

$ext{Total Combinations} = ext{Number of Shirts} imes ext{Number of Hats} imes ext{Number of Scarves}$

Substituting in the values:
$ext{Total Combinations} = 8 imes 6 imes 4 = 192$

Thus, there are 192 different combinations that John can pick.

Step 2

Is he correct? Show your reasoning.

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Answer

John believes that if he picks just two of the three items of clothing (shirts, hats, scarves), there will be more than 192 combinations.

To analyze his claim, let's calculate the combinations for each scenario where he picks two items:

Shirts and Hats:

The combinations will be: $ext{Combinations} = ext{Number of Shirts} imes ext{Number of Hats} = 8 imes 6 = 48$
Shirts and Scarves:

The combinations will be: $ext{Combinations} = ext{Number of Shirts} imes ext{Number of Scarves} = 8 imes 4 = 32$
Hats and Scarves:

The combinations will be: $ext{Combinations} = ext{Number of Hats} imes ext{Number of Scarves} = 6 imes 4 = 24$

So, the maximum number of combinations he can get by picking just two items is 48, which is far less than 192.

Therefore, John is not correct; there will be fewer than 192 combinations when he picks just two items.

14 John has 8 different shirts 6 different hats - OCR - GCSE Maths - Question 14 - 2017 - Paper 1

Worked Solution & Example Answer:14 John has 8 different shirts 6 different hats - OCR - GCSE Maths - Question 14 - 2017 - Paper 1

Show that there are 192 different combinations he can pick.

Is he correct? Show your reasoning.

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