# How many 5-letter words can be formed from the letters of the word mechanical that word always starts with a consonant?

 How many permutations can be formed by the letters of the word, 'VOWELS', wheni there is no restriction on letters?ii each word begins with E ?iii each word begins with 0 and ends with L ?iv all vowels come together?v all consonants come together? Open in AppSuggest Corrections5 The miscalculation is here: the second case was where there were two groups of two alike letters and one different letter. Thus, the number of words formed were: 2C1 . 4C2 . 3! = 72 I assume your \${2\choose 1}\$ implies you are choosing from \$G\$ and \$T\$ and \${4\choose 2}\$ implies you are choosing 2 letters from \$M,N,A,E\$. Your \${4\choose 2}\$ is correct, since you will get two groups of two alike letters, consequently total \$4\$ letters. However, your \${2\choose 1}\$ is not correct (it must be \${4\choose 1}\$), because you can choose not only from \$G\$ and \$T\$, but also from the remaining two letters of \$M,N,A,E\$. Because, a single letter will be a different (unlike) letter. All the rest is fine.