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?

How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all the consonants come together in each word?

How many sides are there in a polygon that has 20 diagonals?