Question

Find the probability of picking 3 consonants and 2 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles.

Answer 1

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

$\frac{21}{26} *\frac{20}{25} *\frac{19}{24} *\frac{5}{23} *\frac{4}{22}$

= 0.02022