The number of ordered pairs (r, k) for which
6.³⁵C_r = (k² - 3). ³⁶C_{r + 1}, where k is an integer, is :

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is :

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to :

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :