If a “word” is any arrangement of 3 different letters, how many 3-letter “words” can be formed from the letters B, O, N, and K, where each letter is to be used once?

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Explanation:

We have 3 slots, which I'll call slot 1, slot 2, slot 3.

Once all the slots are accounted for, we multiply the values mentioned: 4*3*2 = 12*2 = 24.

There are 24 different three-letter "words" that can be formed where any letter selected cannot be reused.

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A slightly different approach:

Order matters because a "word" like BON is different from a "word" like BNO.

Since order matters, we'll use a permutation

We have n = 4 letters to pick from and r = 3 slots to fill.

Apply those values into the nPr permutation formula

We end up with the same result as before.

b

step-by-step explanation:

given

- 2 (3x + 12y - 5 - 17x - 16y + 4 )

simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the parenthesis by - 2

= 28x + 8y + 2 → b