From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

The number of all numbers having 5 digits, with distinct digits is

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