The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be 161700.
Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
The number of ways for a quality-control engineer to select a sample of 3 transistors for testing from a batch of 100 transistors will be
¹⁰⁰C₃ = (100!) / [(100 – 3)! × 3!]
¹⁰⁰C₃ = (100 × 99 × 98 × 97!) / (97! × 3 × 2)
¹⁰⁰C₃ = 50 × 33 × 98
¹⁰⁰C₃ = 161700
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