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Natasha2012 [34]
3 years ago
13

What is the probability that a random permutation of the letters in MATHEMATICS contains the word TEA (with those three letters

appearing consecutively)?
Mathematics
1 answer:
Wewaii [24]3 years ago
5 0

Answer:

The probability that a random permutation of the letters in MATHEMATICS contains the word TEA is 0.04.

Step-by-step explanation:

First compute the number of permutations of the word MATHEMATICS.

There are a total of 11 letters.

And there are 2 Ms, 2 As and 2 Ts

Number of permutations of MATHEMATICS = \frac{11!}{2!\times2!\times2!} = 4989600

Now, if the letters TEA occur together in the same order then the word may be of the form: (TEA)MHMATICS.

There are a total of 9 letters.

The letters TEA is treated as only one letter.

In this case there are 2 Ms.

Number of permutations of (TEA)MHMATICS = \frac{9!}{2!} = 181440

The probability that the letters TEA occur together is:

\frac{Number\ of\ permutations\ of\ MATHEMATICS}{Number\ of\ permutations\ of\ (TEA)MHMATICS} = \frac{181440}{4989600} \\=0.0363636\\\approx0.04

Thus, the probability that a random permutation of the letters in MATHEMATICS contains the word TEA is 0.04.

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