From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist?

How many three digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not allowed?

Let y=x! and z = (2x)! If (z / y) = 120 then what is the value of (3x)!?

Let n be a natural number. The number of consecutive zeros at the end of the expansion of n! is exactly 2. How many values of n are possible?