Question

In how many ways can a consonant and a vowel be chosen out of the letters of the word courage?

Answer 1

There are $3$ consonants {$c,r,g$} and four vowels {$o,u,a,e$} in the word $courage$.

A consonant can be chosen from 3 in ${}^3{C}_1=3$ ways and a vowel can be chosen from 4 in ${}^4{C}_1=4$ ways.

total number of ways consonant and vowel can be chosen is $4\times 3=12$ ways.