Answer: The size of the sample is 840.
The probability that the first three letters of the four-letter code are vowels is[tex]=\frac{1}{35}[/tex]
Step-by-step explanation:
Th total number of letters given to form code of 4 letters = 7
Since, the order of the letters in the code matters, which means there is no repetition.
The total number of ways to form the code size =[tex]7*6*5*4=840[/tex]
Therefore, The size of the sample is 840.
Since, there are 3 vowels and rest of 4 letters are consonant.
The number of ways to form code such that the first three letters of the four-letter code are vowels =[tex]3\times2\times1\times4=24[/tex]
The probability that the first three letters of the four-letter code are vowels is
=[tex]\frac{24}{840}=\frac{1}{35}[/tex]
The probability that the first three letters of the four-letter code are vowels is 1/35 and the size of the sample is 840.
Step 1 - Determine the sample size.
It is to be noted that the total number of letters given to form code of 4 letters = 7
Given that the order of the letters in the code matters, which means there is no repetition; hence,
The total number of ways to form the code size = 7 x 6 x 5 x 4 = 840
Thus, the size of the sample is 840.
Step 2 - Solve for the Probability
Given that there are 3 vowels and rest of 4 letters are consonant.
The number of ways to form code such that the first three letters of the four-letter code are vowels
= 3 x 2 x 1 x 4
= 24
Hence, the probability that the first three letters of the four-letter code are vowels is
= 24/840
= 1/35
Learn more about probability at;
https://brainly.com/question/24756209
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