Out of 7 consonants and 4 vowels, words are formed each having 3 consonants and 2 vowels. The number of such words that can be formed is

If $${1 \over {{}^5{C_r}}} + {1 \over {{}^6{C_r}}} = {1 \over {{}^4{C_r}}}$$, then the value of r is

If $${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84$$ and $${}^n{C_{r + 1}} = 126$$, then the value of $${}^n{C_8}$$ is

The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is