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

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

`(21)/(26) *(20)/(25) *(19)/(24) *(5)/(23) *(4)/(22)`

= 0.02022