The required probability is 0.45
We have total 26 letters in english, of which 21 are consonants and 5 are vowels.
According to the question, we have to select 5 of them of which 4 will be consonants and 1 will be vowel.
Suppose we want to have the vowel in the first selection, so the probability of picking a vowel is equal to the quotient between the number of vowels and the number of total number of letters.
So the probability is 5/26
Now, a letter has been selected, so in the set, we have 25 letters left.
In the next 4 selections, we must select consonants.
In the second selection the probability is 21/25
In the third selection the probability is 20/24
In the fourth selection the probability is 19/23
In the last selection the probability is 18/22
So, the probability is (5/26)×(21/25)×(20/24)×(19/23)×(18/22)
Now, remember that we take that the vowel must be in the first place, but it can be in any five places, so if we add the permutations of the vowel letter we have,
P = 5×(5/26)×(21/25)×(20/24)×(19/23)×(18/22) = 0.45
Learn more about probability here :
brainly.com/question/251701
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, you'll notice this is really just a quadratic equation that can be factorized:
