Question

suppose we want to choose 2 objects, without replacement, from the 3 objects pencil, eraser, and desk. (if necessary, consult a list of formulas.) (a) how many ways can this be done, if the order of the choices matters? (b) how many ways can this be done, if the order of the choices does not matter?

Explanation:

Step1: Calculate permutations (order matters)

The formula for permutations \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 3\) (total objects) and \(r=2\) (objects to choose).

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Step2: Calculate combinations (order doesn't matter)

The formula for combinations \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 3\) and \(r = 2\).

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Answer:

(a) \(6\)
(b) \(3\)