Step-by-step explanation:
picking 3 consonants and 2 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles.
There are 26 letters in alphabet
number of consonants = 21 and number of vowels = 5
We need to pick 3 consonants from 21 consonants
Probability of picking 1 consonant from 26 alphabets = 21/ 26
after picking 1 consonant then number of consonant becomes 20
Probability of picking second consonant from 25 alphabets = 20/ 25
Probability of picking third consonant from 24 alphabets = 19/ 24
We need to pick 2 vowels from 5 vowels
Probability of picking 1 vowel from remaining 23 alphabets = 5/ 23
Probability of picking second vowel from remaining 22 alphabets = 4/ 22
Now multiply all the probabilities
[tex]\frac{21}{26} *\frac{20}{25} *\frac{19}{24} *\frac{5}{23} *\frac{4}{22}[/tex]
= 0.02022
