Respuesta :
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 = [tex]\frac{11!}{2!\times2!\times2!} = 4989600[/tex]
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 = [tex]\frac{9!}{2!} = 181440[/tex]
The probability that the letters TEA occur together is:
[tex]\frac{Number\ of\ permutations\ of\ MATHEMATICS}{Number\ of\ permutations\ of\ (TEA)MHMATICS} = \frac{181440}{4989600} \\=0.0363636\\\approx0.04[/tex]
Thus, the probability that a random permutation of the letters in MATHEMATICS contains the word TEA is 0.04.
