Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair.(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 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair.(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?
Solution
(a) If the order of the choices is relevant, we use the permutation formula. The number of ways to choose 3 objects from 4, when order matters, is given by P(n, r) = n! / (n-r)!. Here, n is the total number of objects (4) and r is the number of objects we are choosing (3). So, P(4, 3) = 4! / (4-3)! = 24.
(b) If the order of the choices is not relevant, we use the combination formula. The number of ways to choose 3 objects from 4, when order does not matter, is given by C(n, r) = n! / [r!(n-r)!]. Here, n is the total number of objects (4) and r is the number of objects we are choosing (3). So, C(4, 3) = 4! / [3!(4-3)!] = 4.
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