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 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 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 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 nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects we are choosing. In this case, n = 3 (pencil, eraser, desk) and r = 2 (we are choosing 2 objects). So, the number of ways is 3P2 = 3! / (3-2)! = 6.
(b) If the order of the choices is not taken into consideration, we are dealing with combinations. The formula for combinations is nCr = n! / [r!(n-r)!], where n is the total number of objects and r is the number of objects we are choosing. In this case, n = 3 (pencil, eraser, desk) and r = 2 (we are choosing 2 objects). So, the number of ways is 3C2 = 3! / [2!(3-2)!] = 3.
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