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Suppose we want to choose 2 letters, without replacement, from the 5 letters A, B, C, D, and E.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is relevant?(b) How many ways can this be done, if the order of the choices is not relevant?

Question

Suppose we want to choose 2 letters, without replacement, from the 5 letters A, B, C, D, and E.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is relevant?(b) How many ways can this be done, if the order of the choices is not relevant?

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Solution

(a) If the order of the choices is relevant, we use the formula for permutations. The number of ways to choose 2 letters from 5 is given by P(5,2) = 5! / (5-2)! = 5*4 = 20 ways.

(b) If the order of the choices is not relevant, we use the formula for combinations. The number of ways to choose 2 letters from 5 is given by C(5,2) = 5! / [2!(5-2)!] = 10 ways.

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