Problem

An electronics store receives a shipment of 19 graphing calculators, including 7 that are defective. Four of the calculators are selected to be sent to a local high school. How many of these selections will contain no defective calculators?
The number of ways to choose all slections that contain no defective calculators is:
Number

Answer

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Answer

Final Answer: 495

Steps

Step 1 :Translate the problem into English: An electronics store receives a shipment of 19 graphing calculators, including 7 that are defective. Four of the calculators are selected to be sent to a local high school. How many of these selections will contain no defective calculators?

Step 2 :Find the number of ways to choose 4 calculators from the 12 non-defective ones (since there are 19 total calculators and 7 are defective).

Step 3 :Use the formula for combinations: C(n, k) = n! / (k!(n-k)!) where n = 12 (non-defective calculators) and k = 4 (calculators to be selected).

Step 4 :Calculate the combinations: C(12,4)=12!4!(124)!

Step 5 :C(12,4)=12!4!8!

Step 6 :C(12,4)=12×11×10×94×3×2×1

Step 7 :C(12,4)=12×11×10×924

Step 8 :C(12,4)=495

Step 9 :Final Answer: 495

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