Test Preparation on Mathematics-Permutation and Combination

The least positive integer n for which _n-1C₅+_n-1C₆ < _nC₇ is _______

n books are arranged on a shelf so that two particular books are not next to each other, There were 480 arrangements altogether. Then the number of books on the shelf is ________

The sum of all possible numbers greater than 10000 formed by using the digits from { 1,3,5,7,9} is

How many words can be formed by taking four different letters of the word MATHEMATICS ?