Question

Among 26 letters, there are 5 vowel letters and the remaining are consonant letters. If three letters are randomly picked out to form a code and the chosen letters cannot be repeated, how many codes, which consist of at least two vowel letters, are possible?

Answer 1

1320

Step-by-step explanation:

The English alphabets have:

5 vowels and 21 consonants.

A three letter code has to be made ans repetition is not allowed and also it must consists atleast 2 vowel letters.

Let's make two cases for it:

2 vowels + 1 consonant

The possible codes = ⁵C₂ × ²¹C₁ × 3! = 10 × 21 × 6 = 1260

3 vowels

The possible codes = ⁵C₃ × 3! = 10 × 6 = 60

Total possible codes = 1320