In how many ways

To find: number of ways in which a vowel, a consonant and a digit be chosen out of the 26 letters of the English alphabet and the 10 digits.

e.g.

Way of selecting a vowel from 5 vowels=⁵C₁

Way of selecting a consonant from 26 consonants=²¹C₁

Way of selecting a digit from 10 digits=¹⁰C₁

So ways of choosing a vowel, a consonant, a digit=⁵C₁ × ²¹C₁ × ¹⁰C₁

=5 × 21 × 10

=1050