Assembling a computer

Sam is going to assemble a computer by himself. He has the choice of chips from two brands, a hard drive from four brands, memory from three brands, and an accessory bundle from five local stores. How many different ways can Sam order the parts?


The answer is 120.

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1 solution

If an operation can be performed in n 1 n_1 ways, and if for each of these a second operation can be performed in n 2 n_2 ways, and for each of the first two a third operation can be performed in n 3 n_3 ways, and so forth, then the sequence of k k operations can be performed in n 1 n 2 . . . n k n_1n_2 ... n_k ways.

Since n 1 = 2 , n 2 = 4 , n 3 = 3 n_1 = 2, n_2 = 4, n_3 = 3 , and n 4 = 5 n_4 = 5 , there are n l × n 2 × n 3 × n 4 = 2 × 4 × 3 × 5 = 120 n_l\times n_2\times n_3 \times n_4 = 2\times 4 \times 3 \times 5 = 120 different ways to order the parts.

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