Mathematics, 08.03.2021 04:00 Animallover100

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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Answer from: daniel9299

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Explanation:

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

For slot 1, we have 4 choices to pick fromThen slot 2 has 3 choices since we can't reuse a letterFinally, slot 3 has 2 choices. We count our way down each time we move to the next slot.

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

$_{n} P_{r} = \frac{n!}{(n-r)!}\\\\_{4} P_{3} = \frac{4!}{(4-3)!}\\\\_{4} P_{3} = \frac{4!}{1!}\\\\_{4} P_{3} = \frac{4*3*2*1}{1}\\\\_{4} P_{3} = \frac{24}{1}\\\\_{4} P_{3} = 24\\\\$

We end up with the same result as before.

Answer from: Quest

B? ? i'm most likely wrong but i think it would be b
Which two-dimensional shape is formed if a plane intersects the cylinder shown, perpendicular to the

Which two-dimensional shape is formed if a plane intersects the cylinder shown, perpendicular to the

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

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If a “word” is any arrangement of 3 different letters, how many 3-letter “words” can be formed from...