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# help probability

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Four letters are selected at random with replacement from the word MATHCOUNTS. What is the probability that the letters in the order they are selected will form the word NUTS?

Oct 13, 2022

#1
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Here is my attempt:

MATHCOUNTS ==10 Letters with 2 "Ts" gives us 9 distinct letters:

Drawing 4 letters at random, gives the following number of permutations:

Since the letters are replaced (or repeats are allowed), then we have:

9 x 9 x 9 x 9 ==9^4 ==6,561 permutations

Since the letters: N U T S can appear in 4! ==24 permutations, then:

The probability is: 24 / 6,561 ==8 / 2187==0.36579789 67 %

Note: somebody should check this!!

Oct 13, 2022
#3
+118652
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Four letters are selected at random with replacement from the word MATHCOUNTS. What is the probability that the letters in the order they are selected will form the word NUTS?

This is what I think.  Sounds correct to me.

1/10 * 1/10 * 2/10 *1/10 = 2/(10^4)  = 2/10000  = 1/5000  = 0.0002

Oct 14, 2022