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Suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp.

(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?
PLEASE HELP

User Davmos
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1 Answer

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Explanation:

(a) If the order of the choices is relevant, we can choose the first object in 5 ways, and the second object in 4 ways (since we cannot choose the same object again). Therefore, the total number of ways to choose 2 objects without replacement and with order being relevant is:

5 x 4 = 20 ways

(b) If the order of the choices is not relevant, we need to use the combination formula, which is:

nCk = n! / (k! * (n-k)!)

where n is the total number of objects, and k is the number of objects we want to choose.

In this case, we want to choose 2 objects out of 5, so n = 5 and k = 2. Therefore, the number of ways to choose 2 objects without replacement and with order not being relevant is:

5C2 = 5! / (2! * (5-2)!) = 10 ways

Therefore, there are 20 ways to choose 2 objects without replacement and with order being relevant, and 10 ways to choose 2 objects without replacement and with order not being relevant.

User Vertexwahn
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