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 taken into consideration?(b) How many ways can this be done, if the order of the choices is not taken into consideration?
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 taken into consideration?(b) How many ways can this be done, if the order of the choices is not taken into consideration?
Solution
(a) If the order of the choices is taken into consideration, we are dealing with permutations. The formula for permutations is P(n, r) = n! / (n-r)!. Here, n is the total number of objects (4 in this case: pencil, eraser, desk, and chair) and r is the number of objects we are choosing (3 in this case). So, P(4, 3) = 4! / (4-3)! = 24.
(b) If the order of the choices is not taken into consideration, we are dealing with combinations. The formula for combinations is C(n, r) = n! / [r!(n-r)!]. Here, n is the total number of objects (4 in this case: pencil, eraser, desk, and chair) and r is the number of objects we are choosing (3 in this case). So, C(4, 3) = 4! / [3!(4-3)!] = 4.
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