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Akimi4 [234]
2 years ago
7

You are creating strings picking letters from the English alphabet at random. What is the probability that your randomly created

string of length 11 will contain exactly 7 A's
Mathematics
1 answer:
White raven [17]2 years ago
8 0

There are 4 positions in the string that each have 25 choices (any letter in the English alphabet except A) and the other positions are filled with A, so there are 25⁴ possible strings containing exactly 7 A's.

Overall, there are 26¹¹ possible strings of length 11.

Then the probability of randomly generating a string containing exactly 7 A's is

25⁴ / 26¹¹ ≈ 0.000000000106427

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I'm assuming you meant to write a^4 = 625.

If that is the case, then note how 625 = 25^2, and how a^4 is the same as (a^2)^2

So we go from this

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Apply the square root to both sides and you'll end up with: a^2 = 25

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a^4 = (5)^4 = (5)*(5)*(5)*(5) = 25*25 = 625

Both values of 'a' work out

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