Question

The word geometry has eight letters. Three letters are chosen at random. What is the probability that two consonants and one vowel are chosen?

Answer 1

Answer:
`(15)/(28)`

Explanation:

The given word : geometry

Total letters in the above word = 8

Number of vowels (a e i o u) in word =3

Number of consonants = 5

Number of ways to choose two consonant and one vowel is given by :-

`F=^5C_2*^3C_1\\\\=(5!)/(2!(5-2)!)* (3)\ [ \because ^nC_1=n]\\\\=5*2*3=30`

Number of ways to choose any three letters from the 8 alphabets:-

`T=^8C_(3)=(8!)/(3!(8-3)!)=8*7=56`

Now, the probability that two consonants and one vowel are chosen :-

`=(F)/(T)\\\\=(30)/(56)=(15)/(28)`

Hence, the required probability =
`(15)/(28)`