Compute \({}_7P_3\).

Answer: \(7\times6\times5=210\).

Compute \({}_8C_2\).

Answer: \(\frac{8\cdot7}{2}=28\).

How many 3-letter arrangements from A,B,C,D (no repeats)?

Answer: \({}_4P_3=24\).

How many ways to choose 3 students from 10?

Answer: \({}_{10}C_3=120\).

A 5-card hand from 52 cards: probability all hearts.

Answer: \(\frac{{}_{13}C_5}{{}_{52}C_5}\).

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